I built a few "Super XTs" back in the 90's (when it was more politically correct) and I'll have to say from my experience that if you're *not* willing to hack on the case a little your options are pretty limited. The problem you'll run into trying to fit most "Baby AT" motherboards into a 5160 is there simply isn't enough space under the drive bay to slide them under it. They almost inevitably will have components like SIMM sockets, voltage regulators, the CPU itself, etc, that are just too tall. I dealt with that back in the day by simply hacksawing out a corner of the bay but, yeah, you probably don't want to do that now. They did sell those little one half/two-thirds size AT boards that were only a couple inches longer than a 16 bit ISA slot, you could try measuring it out and seeing if one of those would fit. The only one I had back in the day was a truly tiny 386SX board and that certainly did fit, but I'm sure you want to go higher than that.
Note that even if you do go with a really short board that doesn't make you cut the metal you still probably won't be able to use the middle drive bay, at least not with a device resting on the floor of it. On the ones I built I hacked together a little shelf to let me stick a 3 1/2 HD into the space over the bay.
The best Baby AT boards I've ever laid hands on myself have been K6-2 Super Socket 7's, but I've heard rumors that Socket 370 boards do exist. I suspect it'd be hard to go any higher than that without really thinking outside the box and going with something like a single-board industrial computer with a passive backplane in place of a real motherboard. The sky would be the limit there, although it would probably limit your video card choices and those passive backplane computers are *expensive*.