IMHO you're always better off converting a quick release rear to a solid axle, because:

I've ridden a QR rear on a track for training. The QR would slip and require readjustment every now and then. This is without any real abuse and I'd seriously doubt you could skip and skid on one with much confidence. This could have been just a worn out/cheap QR or paint issue but it really was no fun.

I've also broken 'cheapo' qr axles on a singlespeed before. Solid axles are just a little beefier.

Its much easier to service a non-qr wheel as you don't need to allow for axle flex (this a pretty pathetic excuse though).

But I think the perception that it could slip, would probably play tricks with your mind, thus ruining your ride as you'll just keep checking your chain tension