Finally managed to get it working on the BBB.
The main problem is that the BB helpfully wants to capitalize the first letter of any input field. Extremely useful when you're entering in contact information, really sucky when you're trying to enter in case-sensitive usernames and passwords. The quick hack I found to get around it is you hit the key you want, backspace over the capital letter, then hit again and you get the lowercase. And, no, holding down the shift key doesn't work.
I had to go with the "latest development" version 1.7.3 because it supported SSH2. Also had to twiddle around with the fonts (8x16 seems to be readable).
By default, midpssh wants you to open up a seperate screen and enter in any commands there as a kind of batch deal, but it's possible to type directly to the console by setting the input type in the options menu. It's kind of clunky and I'd hate to have to try and use vim with it, but it's good enough for restarting services in a pinch.