First of all, welcome to the board @BosMaineiac
! Always great to see new faces around here.
Likewise, always great to see another supporter of NSRL! And I like the imaginativeness you've brought to the topic -- that's always an important part of the discussion.
I share your interest in resurrecting that straightaway along the Eastern Route that runs pretty much directly from Lynn (!) all the way to the current Airport station. It is incredibly tempting, especially from a "neat and tidy" perspective. It's just right there.
And as others have noted, there once in fact was a proposal for exactly the kind of cross-harbor tunnel you are describing here between South Station and East Boston. You can see a map of that here on Wikipedia (although ironically they would have hooked this tunnel into today's Blue Line, rather than into the straightaway).
I like the thinking behind incorporating an East-West dimension into the Rail Link concept, but I think it's ultimately unnecessary for a few different reasons.
First, the time/distance savings just aren't that much; I did some back-of-the-napkin math, and from what I can see the best case scenario is shaving a 15-minute journey into a 10-minute journey (with non-trivial drawbacks -- see below).
Second: you argue that this East-West link would reduce the need for BLX to Lynn, but I'm skeptical. One of the arguments in favor of a North-South link is that it would allow northside riders better access to downtown, which North Station is more removed from than South Station. But South Station itself still isn't the be-all-end-all. Many riders have destinations outside of the Financial District (which is better served by the Blue Line than South Station anyway), and the Blue Line (assuming a Blue-Red connector) offers much better transfer opportunities than an East-West tunnel to South Station would; such a tunnel would dump all of its riders on to the Red Line, who would then need to traverse the already-most crowded section of the line. Plus, South Station-Longwood Medical Area is a significantly more awkward journey than State/Gov't Center-Longwood Medical Area (and more on that in a second, too).
And that brings us to another drawback of a cross-tunnel routing -- it avoids a transfer node at Sullivan which can distribute Cambridge- and Somerville- (and maybe even Allston-) bound riders without going downtown, and it actually results in a trajectory that, overall, misses downtown much more than a Chelsea-Sullivan-North Station-South Station alignment would.
Third (and I'm surprised this hasn't been brought up yet): how exactly would things work at South Station in terms of that X-shaped network you've drawn? Is it a Camden Town-style double flying junction, with essentially two stations allowing all trains to go everywhere? Is it like District Line Earl's Court with a single unified station with flying junctions before and after? Or do you abandon "all trains go everywhere" and split the network into a North-South network and an East-West network with separate superimposed stations à la Notting Hill Gate? Or with cross-platform transfers akin to Finsbury Park?
The reason this matters -- aside from the potential for an incredible amount of spaghetti under there -- is that you have to trade-off between the network comprehensiveness of "all trains everywhere" and the speed reductions incurred by crossovers, curves and capacity constraints. Plus, it impacts passenger journeys: you could mitigate some of that Red Line transfer crush if you can guarantee some x % of trains will travel Airport-Back Bay, Airport-Ruggles and Airport-Lansdowne, but again, that is going to entail a much more complicated build. (Plus, addressing the needs of incoming Airport riders impacts riders from the other direction as well, shunting away trains that might otherwise serve downtown more directly.)
^ Okay, so there are challenges with this -- any infrastructure proposal has challenges; the question is whether it's worth the benefit.
And that brings us to this (emphasis mine):
This lurks in the background of your proposal, and I want to examine it further. What exactly is the benefit of creating all this infrastructure for the benefit of the Eastern Route? (Setting aside access to the airport.)
Put another way, why would Amtrak run trains along the Eastern Route? The Western Route ends up getting you to the same place in Southern Maine, and has the benefit of hitting Haverhill/Lawrence and UNH along the way. Newburyport is practically a seaside village by comparison. Moreover, when leveraged with the Wildcat Branch, as the Downeaster currently does, a Western Route alignment can bootstrap itself to the Main Line (Lowell Line), which is the much stronger candidate for Amtrak expansion into New Hampshire (Nashua, Manchester and Concord).
(And, indeed, on the 100-year timescale, an alignment via Lowell is where Boston should be looking for its northern expansion -- follow that alignment long enough and you hit Montreal; there's nothing comparable north of Newburyport and there almost certainly never will be.)
So, in summary, while I like the idea for its creativity and imagination, I'm pretty skeptical of its ultimate benefit.
So the one big benefit that I haven't addressed is better access to the airport. There's a larger political and theoretical debate here that I'm not qualified to weigh in on (about the merits of intercity rail-airport connections). But I will happily and generally agree that better public transit access to Logan is a Good Thing, even if I'm agnostic on where it should rank on the priority list.
Your proposal calls for a massive investment in a cross-harbor tunnel to provide transfer-minimal public transit access to Logan. Let me propose an alternate version of the same.
Instead of a mainline rail tunnel hooked into the NSRL, construct a roomy third tunnel along the Ted Williams Tunnel alignment that can support light rail, BRT and intercity buses. Hook it in directly to the existing Silver Line Transitway tunnel (along with a connection to the I-90 tunnel for those Greyhounds and a surface portal) and convert the Transitway to dual BRT/LRT running. If you have extra money, expand the Transitway into "four tracks/four lanes" to support non-stop South Station-Airport Terminals services.
On the other end, hook the tunnel into the mode of your choice -- continue running BRT to the terminals at street level, build an elevated LRT in lieu of the APM, construct an APM/LRT transfer station along Harborside Dr, what have you. Personally I think the ideal would be integrated LRT all the way -- not saying that you use long-haul South Station-Chelsea LRT service as a terminal shuttle -- you probably want to have some dedicated short-turns -- but that seems like it would give maximum flexibility.
For local public transit, a third TWT would obviously be a boon, speeding access and reliability to Logan from the Seaport, Southie and the South End, closing the one section of the Urban Ring Corridor that's Really Hard™ to put rail into. Moreover, a dual LRT/BRT tunnel would give maximal flexibility for metropolitan connectivity -- the downside of a mainline rail tunnel is that you can only put electrified mainline rail through it. A properly designed dual-mode tunnel could support a veritable smorgasbord of urban and suburban and regional services.
For regional access to the airport, a third TWT would I think ultimately be more beneficial than an East-West Rail Link. Assuming an NSRL, all suburban quadrants would have direct access to South Station, from which it'd be a single transfer to direct terminal access; by contrast, under an EWRL, only North Shore riders and whichever service(s) from the south get paired would have access to Airport Station, from which they'd still need to transfer to the APM.
A dual-mode tunnel also gives you a lot more flexibility with alignments and grades. When working with mainline rail, you have to deal with longer platforms, gentler grades and therefore longer approach tunnels. A dual-mode tunnel gives you a lot more flexibility both at South Station and at the airport.
Finally, it's worth pointing out that while South Station may seem far away from the airport, it really isn't. An express South Station-Airport service would only travel ~2.75 miles. The JFK AirTrain from Jamaica Station in NYC travels a bit less than twice as far. (And, of course, Jamaica Station itself is already between 20 and 60 minutes from Manhattan, depending how you travel.)