Are you sure that you've switched banks in the multi-instrument? It should work just as you described. Seeing as you're able to get one of the banks working, I would suspect that either a) you are not switching the banks in the multi-instrument or b) you are switching banks but have not set up the bank select messages correctly in the multi-instrument.
If the multi-instrument is one that you have created, try going to www.swiftkick.com
for some Logic environments. There should be a JV-1010 environment there which should have an appropriate multi for you. All you would need to do then is assign the appropriate midi port for it and away you go.
Also, try subscribing to the online mailing lists for Logic Audio and Sounddiver. You can find these at www.yahoogroups.com.