So the biggest issue with your reaches is money - even if you got in, you’re not getting any…or likely not a lot.
GW may or may not be a match. I lot will depend on how much interest you show. But given you are not a popular major, it may help.
If he loves DC, then how about American…it’s not in the heart but it’s there…or even UMD. American, like GW, you’d need to demonstrate interest and UMD is not a match but a reach - albeit not a high reach.
In regards to LACs and outdoors, I already mentioned Sewanee - which would get you everything you listed - outdoorsy, merit, etc. Merit for you is important - because if he’s truly going to law school - and you can’t know that - know that where he goes matters far less than what he does (GPA, LSAT) in regards to law school. I say this because this year Harvard Law is represented by 174 undergraduate schools - including Cal State Northridge and LA, Bloomsburg of PA, Fairleigh Dickinson, U of you name it - Arkansas, Kentucky, WVU, St. Johns, Stetson, etc. Yes, you’ll see more students from top schools - but likely for the same reason they went to top schools to begin with - they were the top students then and are now - and that bodes well for you based on test score. Top students are top students but many do choose undergrads for different reasons - location (to home), cost, other thing - but I would not say that means, by itself, going to a top school gives you a better chance per se.
So - if you have a budget, don’t justify a higher cost such as - my budget is X but I’ll apply to Davidson which costs X + Y.
LACs that might be outdoorsy in addition to Sewanee - and I suppose it depends what you mean by outdoors - hiking, skiing, biking, etc. but you might also look at and these are safeties - but safety/match doesn’t matter - fit matters - Bard, Willamette, Lewis & Clark, and Eckerd (for beach).
For an off the wall suggestion and not sure about merit, check out St. Johns College in Santa Fe.
For some reasonably priced smaller schools - I think UNC Asheville was previously mentioned. How about Western Carolina - tuition $5K + fees - so I think $8K and very outdoorsy. Adams State in Colorado would be another. For mid size, UT Chattanooga could work and for likely cheaper than Colorado but a big school, U of Tenn in Knoxville could be a sub…not in regards to skiing but equally close to great hiking, etc. Then again, Utah would be Colorado - and much cheaper as would U of New Mexico. Colorado is over $60K and most get a small scholarship - $6250. For really outdoors, how about Montana State in Bozeman or U of Montana in Missoula…and all will be cost competitive relative to names you mentioned. These type schools are also smaller in population so not small - but not 20K+ kids either…more mid size - so U Montana 11K students for example.
That your son is a good test taker bodes well for law school - because he’ll do well at the LSAT which far outweighs, at least based on what I’ve seen, his undergrad school.
Best of luck.