If you are having to ease and sheet more than one arm pull then you are overpowered. Depower your rig with downhaul (main and jib), outhaul, and mast rotation so that you only have to ease a couple of feet (or less) on the main sheet.

I almost always have a wrap or two on my hand and have never had a problem getting out of them in a hurry. If it's windy enough to double trapeze, the crew on my boat usually handles the mainsheet.

For getting out on the trapeze, I hold the tiller and the mainsheet (with some slack) in one hand while I hook in and push out. I slide my hand up the tiller extension while pushing out and bring the sheet with me. Then I grab the sheet so I have tiller in one hand and sheet in the other. Meanwhile, I'm prepared to pinch up to depower while vulnerable in this position. However, if sailing with crew I usually hand the mainsheet to them over my shoulder and outside of my main bunji just before pushing out.