Originally Posted by MacG
QR axles work best in short vertical dropouts where the weight of the bike and rider holds the axle snugly in the dropout and there is no forward space in the dropout for the chain tension to slide the axle into. Putting a QR axle in a horizontal dropout can be done. but you need to get them pretty dang tight and still will probably experience some slippage when pedaling hard (or more likely from skipping hard).
My suggestion is to just carry a peanut butter wrench and deal with it. It is a ton easier to adjust chain tension exactly with a nutted axle because you can lock one side of the axle down snug and use the rim as a lever up near the bottom bracket to move the other side of the axle back and forth in the dropout in a very controlled manner. I think setting chain tension is annoying enough with a nutted axle and this technique, so I would hate to have to do it with a QR axle where the whole wheel is flopping all over the place while you're trying to get the chain tension down dead nuts. Just my opinion...
QR's where used for years in horizontal dropouts becasue they worked well enough under normal riding conditions. It may slide forward a bit under skidding pressure but if you use the right qr or ust toothed washers it should be fine especially since the OP has two brakes.
You shouldn't need that much accuracy in adjusting wheel tension. Holding it back and clamping down when its centered should be enough. If thats too hard you can hold in the front beteen the chainstays so as to center it easier. Since this is about a conversion the screws in the dropout(if they exist) can be set to the right position to make it even easier.