There is a ton of low pressure cartridges you can run in one as I'm sure you know. I'd have to say the 6.5x57 or .444 Marlin just because of the size of the action. My first thought is to do the 6.5 because there would be no modification to the action other than a rebarrel. My next thought is how much performance gain am I going to get over a 6.5X55?
That leads me to the .444 Malin which is the next longest (and great case IMO for wildcats). I think it would make an excellent short range thumper of deer and other game. I've never shot the .444 in its original form, I've ran some wildcat cartridges like the .358 and .375 JDJ which were awesome to shoot.
I went through the whole gambit of what to build on an old bubbaed 93 as well a few years ago. I wound up letting money decide, as I found a new $40 barrel short chambered in .30-06 but for a small ring mauser. I had the threads cut off, rethreaded for a small ring and chambered in .300 Savage. Neat little cartridge and rifle now that I do enjoy shooting I just wish I got to work with it more.