I have successfully used Campagnolo Ergopower shifters with a 22/36 MTB crank. It took a little fiddling to get things adjusted properly, but it worked well once everything was sorted. You may be able to run a similar setup with your current components.

Sugino has sub-compact doubles (ex: OX601D) that would be compatible with your Shimano shifters.

SRAM's 10-speed road levers are compatible with their 10-speed MTB rear derailleurs, and the latter can easily handle 36t cogs. This doesn't help you now, but if wanted to swap out your current 9-speed components, it's worth considering. You could also try a 9-speed Shimano XT rear derailleur with a Shimano 36t cassette.