Having such a small garden .......................

What about some pictures Dave ?
Jenny "~))

bursts into laughter Anyway. Dave, did some googleing. Check out:
1. http://www.virtualmuseum.ca/~mushroo.../glossary.html
Apparently fungi can speed up de-composition.
2. http://pubs.caes.uga.edu/caespubs/pubcd/C764-w.htm
Apparently nitrogen speeds up de-composition.

I also read an article where they said that it would not make sense to
plant legumes and then plow them under and then plant crop immediately
because the de-composing veg matter would hog all the nitrogen.

You could try dusting the chopped banana-stem in a Nitrogen-fertilizer
and placing it seperately in a corner of the compost pit where it's
nice and warm, with plenty of veg matter and purchased fungi. Link 1
has names of fungi..or just wiki that.

Give us the results - if you try this !