I friggin found one that works!
Tech 21 XXL (weird, the sansamp I used in front of it occasionally was even worse than most pedals) seems to have enough definition in the low end that you can dial out all the highs and it still sounds fucking awesome.
The sound I get out of it into a totally clean Twin Reverb (volume set just under 2, so the tubes aren't even working very hard yet) reminds me of a JCM-800, but grittier and a bit bassier. Sounds even better when I push the Twin a bit (even at low volumes) with a boost.
This is a major breakthrough for me, and I know a lot of other people with Twins have constantly faced this issue.
QUESTION, TOO (QUESTION TWO!)
Anyone suggest any good boosts? I am pretty close to doing my usual "don't overthink it - MXR Micro Amp duh," but maybe there's something boutiquey that is just that much better. Right now I'm using my Line6 Crunchtone, and it does a fairly good job. Colours it a bit too much, but it has a built-in noise gate which is a huge help. Any favourites out there?