If the calcs I did are correct, cross bracing won't do s...t for your
situation.

From a vibration point of view; 2x10's spanning 15' appears to be way
undesized.

here is a link to a report that discusses this type of problem

http://irc.nrc-cnrc.gc.ca/cbd/cbd173e.html

taken from the report

"Studies of light joist (wood or steel) floors with wood deck, in
progress at the Forest Products Laboratory at Ottawa, indicate that for
spans up to 15 feet acceptable vibration performance for most
residential occupancies is obtained if the static deflection does not
exceed 0.05 inch under a point load of 220 lb."

also

http://www.inspectamerica.com/html/bouncing_floors.html

I calc that your joists will deflect ~.19 under a 220 lb point load or
nearly 4 times more than desireable.

Maybe I made a mistake on the calc but the current floor behavior seems
to agree with the calc.

cross bracing will provide little or no gain.

IMO you need to glue & nail (or screw) a 2x6 flat to the bottom edge of
the existing joists and that will get you down to ~.07" (not perfect
but much better)

Pre drill the 2x6 with a clearance hole do you get good clamping effect
on the glue. I'd prop the joist slightly so the system is preloaded
when you remove the prop. Wait until the glue drys.

cheers
Bob