How about combining the split idea with a lottery? Choose 1/3 of license holders at random and grant them a split. If the demand was inelastic, the winners each get a small windfall and we have a strong signal to repeat the process. Nobody should be too angry at this point. The second lottery excludes the winners of the first lottery and the licenses generated by the split. This time you draw half of the remaining original licenses (i.e. another 1/3 of the original pool) and monitor the sale prices. If the sale prices remain high, do the final 1/3. If at any point the sale price drop so low that the split is deemed punitive, then stop or take a break for a couple years until there is a “new normal” that has stabilized at the lower price.
At some point, maybe even from the very start, all license holders will oppose the added competition of the new licenses generated. But as long as the split is guaranteed to generate some value for the original license holders it could be deemed fair and in the public interest by policy makers. That might be necessary to stave off lawsuits. Perhaps there is some other offset that can be offered to license holders such as a tax credit or something.
Alternatively, instead of choosing a fraction of existing holders to grant a full split, you could grant all holders a fractional split. So instead of 1/3 of existing holders getting a full license split to sell, all existing holders could get 1/3 of a license split to sell. This is more fair because there's no winners and losers of a lottery, but a bit more complicated to execute in that you need the additional step of combining shares before they can be brought to market. The "market maker" here who would combine the fractions into whole licenses to sell would most likely be a third-party broker working on behalf of the existing establishments. And since people are generally risk averse, you'd probably find that existing license holders would prefer a guaranteed value of one-third of x to a 1/3 chance of the full value of x. (You might even see an insurance market pop up in the event of a lottery, where existing holders could hedge their risk and sell their 33.33% lottery ticket for a guaranteed return of <33.33%, with the insurance provider netting the delta).
Or the City could just create new licenses and auction them off, then distribute that revenue evenly to all existing holders. As an example: the NBA currently has 30 teams, and is considering expanding to possibly 32. The way this would work is that the league itself would create two teams to sell to (pretty much) the highest bidders, and then that sale price revenue from those new teams would be divided among the existing 30 teams. So if the NBA allows for two expansion teams and sells the rights to them for $2 billion each, then each of the existing 30 owners will get ($4 bill / 30 teams) = $133 million each from it. If I'm an existing owner I like that upfront cash (especially during a pandemic) and I like that the expansion teams will grow the league across the country (bringing in additional fans and money from cities that don't currently have an NBA team such as possibly Seattle and Las Vegas). But if I'm an existing owner I also don't like that the expansion will dilute the market value of my team by increasing the supply of teams, and I don't like that that pooled NBA revenue that is granted to the teams (like national TV deal and sponsorship dollars) will now be split 32 ways instead of 30. Sound familiar?
The problem with a City-sponsored auction is that I don't think it would play well politically. The pure market mechanics of it would surely be objected to and muddled with on equity grounds, and you'd end up with some sort of multi-criteria analysis that adds other factors to the scale for license distribution and ends up decreasing the return for existing holders. That's why I think a pure split is the cleanest and easiest way to implement it, and best way to achieving the end goal of increasing the supply of licenses while reimbursing existing license holders.
Any one of these schemes would require a change to State law, because the number of transferable liquor licenses in the City of Boston is capped by the Commonwealth, not by the City itself. And if any of these schemes were to implemented, I'd think it'd have to go along with sunsetting the recent allocations of non-transferrable neighborhood-specific licenses that do not fall under the State-imposed cap. Those were always a work-around of the State cap, and with a change in State law such a work-around would no longer be necessary.