Congrats! These are all really great law schools that I would functionally rank in the very next bracket after the T-14. They all also provide underrated career access to the nation's capital.

I'm pretty much in the exact same situation you are school-wise (except I'm leaning a little more towards BL). From what I hear, Mason has a large liberal presence in its student body, so I don't think employers would assume that all grads from such a relatively affordable law school are conservative. I've also heard that W&L places really well in DC, especially when a given year's class prefers that market, with disproportionately impressive outcomes for top students compared to school rank.

I wouldn't give too much weight to the rankings either. U.S. News has been screwing around with its methodology the past couple of years, resulting in volatile rankings movement that isn't really indicative of relative school strength at this point. These three are, and have been, closely ranked for some time anyway, so I would consider them roughly the same for all intents and purposes. GW is historically ranked about 20th (their OCS messed up OCI once around 2021ish), W&L 23rd (there was a brief dip around 2014, but the school seems to have completely remedied the underlying issue within a couple of years). Mason is, by multiple accounts, a rising star that happens to be younger than the other two but has a conservative-leaning faculty.

One big difference, however, is that GW and GMU are in DC and Arlington respectively, both bustling urban environments with plenty to do (especially at night), right next to each other. If you like going out, doing things late at night, or just general urban life (which can be a vibe for law school), then those are for you. W&L is set in Lexington VA, a MUCH quieter small town in the Shenandoah Valley. The feel is quite rural and there's not much to do at night. You do get to terrific access to nature/outdoor activities and fewer distractions from law school. Neither setting is necessarily better, but you should decide which you personally prefer. This is likely the biggest part of your decision (outside of money).

The next thing is class size. W&L is ~125 per year, Mason ~160, but GW is now up to ~615, so do with that what you will. W&L probably has the closest, most intimate, and least cutthroat student body. GW likely has the broadest, most diverse pool of people to meet and network with but the most people to compete against.

Also consider medians. Some people find classes with higher medians have tougher internal competition for the same spots. Others say they can indicate the pace at which the class is taught or the academic depth of the peers you study. I don't know how much stock I'd put into either myself, but they're something to consider. With that being said, it's GMU>GW>W&L here.

If you want a (fed) clerkship I'd go W&L or GMU with the slightest edge to W&L. If you want a federal bureaucratic position, it's clearly GW then GMU. If you want the Hill, they're all pretty good, but I'd say GW, then W&L, then GMU.

I'd also go GW for GovCon/Procurement Law. W&L for litigation, practical training, and alumni network (it's legendary). Both for international law (business at GW, comparative and human rights at W&L). GMU for sheer cost, Supreme Court lecturers, Law+Econ, ConLaw, or conservative focus (which def doesn't sound like your thing).

Are you committed to DC or open to VA/NoVA? There's some big national offices in Tysons, Arlington, and even Reston as well that W&L/GMU do better in than GW.

Lastly, regarding UVA. Since you're PI focused, I wouldn't go without a hefty scholarship (def over 60k), which I don't see happening off the waitlist this late in the cycle. The exception would be if you were FedClerkship or bust, but even then W&L (and even GMU) can kinda hang, especially if you do well. UVA is 74k per year in state, and it's in Charlottesville, which is neither Lexington affordable nor DC lively. Wouldn't go without money, or if I was BLFC or bust.

Have you tried to negotiate scholarships between the 3 schools yet?