Others have covered a lot of this, but here is my two cents:
$400K is great, but not nearly enough to cover full pay private for undergrad and then med school, and I would never recommend a young person pay the implied difference for their education themselves.
OK, so personally, I would eliminate every private college or OOS public which doesn’t have merit. I know that is a lot of famous colleges, but I just can’t recommend them at what it would end up costing you personally.
Fortunately, you do have a strong merit profile, so if you want to keep on the longshot merit privates, that is fine.
And then you could do just those and your UCs/CSUs.
However, there are privates where you would have a much bigger chance of a lot of merit.
We’ve already mentioned Rochester and Case, which could be considered, although the odds of getting enough merit from them to compete with your likely UC options might be a little slim still. Case might be your better bet, though, IF you demonstrate a lot of sincere interest.
OK, so how about some LACs? Again they can be great premed options, and long story short, they are often better bets to give enough merit to compete with in-state COAs, and sometimes actually beat them.
Washington and Lee and Richmond are two that sometimes give BIG merit. Again the odds are not the best, but you have the profile to realistically try if you would like. I’d suggest the odds of getting BIG merit from one of them is a notch higher than from the WashU/Emory/Vanderbilt sort of colleges, so maybe worth a shot?
Then there are some which give at least enough pretty big awards that they could be well worth considering. Some you could consider would be Kalamazoo, Juniata, Earlham, Allegheny, Rhodes, Trinity (Texas), and St Olaf. This may seem random, but it isn’t–these are all popular possibilities for premeds in my circles, and/or Bio kids, with robust merit programs. All of these in particular also offer Neuro (I note at Kalamazoo and St Olaf, it is an interdisciplinary concentration, as opposed to a major, but that is sort of their thing anyway).
But again, you could just do mostly UCs/CSUs. It can be nice to have choices, though, particularly if some of those choices actually would beat in-state COA.