Pointing out the obvious: No trucks allowed on most/all of the river roads inbound from there - Nonantum, Greennough, SFR, Memorial, etc, nor on a lot of the rest of the parkways.
North Beacon/Brighton Ave, Arsenal/Western yes, but I think it's somewhat obvious that it's probably not a very worthwhile/effective toll or traffic dodge for a heavy truck with the much more limited routing options vs a car.
The only other sort of sane + legal routes for a truck to supply anything in that region (say, the Arsenal Mall) are some limited routes over from Route 2 that are much longer and obviously worse, even with Galen St's traffic nightmare.