Nick I've never biked off the Midi, I've skied a couple of routes from the mid station which finish on walking trails but I am pretty sure the top sections would just be meadows or gulleys in Summer, and its a couple of years since I was up there.
I was there in August last year, with limited time on my hands but I might give it a crack this year. Depending on the lifties and how busy it is I reckon they would probably let you on the lift, as long as you got out at the mid-station.
That side is quite steep so I would pick something that doesn't lose elevation too fast or you'll be carrying down. There is a big traverse over to Montenvers from the mid station. From Montenvers there is a trail which is pretty much all descent, but not too steep, coming out at Planards, that might be a good bet but it could be a mess of rocks and roots up towards Montenvers.