Hi Simon,
I'm sorry I can only be brief as I'm about to leave for the airport. I think I may have mentioned that I study Muso Jikiden Eishin Ryu and Toda-ha Buko Ryu (which also includes sword work but focuses on the naginata). As you know, MJER is a very big school so there is a rather wide variety of preferences, not only with respect to swords but also with respect to executing techniques.
Nevertheless, it is generally important to match your sword length to your height (or arm length) so that the MJER nukitsuke (drawing of the sword) can be performed correctly. If your sword is too short it will fly out of the saya, if it is too long you will have to do contortions to get it out. Some people check the length of a sword by holding it loosely in their right hand with their arm relaxed at their side - the tip of the sword should just touch the ground in front of your feet.
I know I haven't really answered your question about schools that favour short swords. However, if you ever want to give MJER a try, I am happy to take you to my dojo in the Jiyugaoka area of Tokyo (several of the guys there are sword collectors so you should feel at home).
Cheers,
Matthew