Junction Hollow feels safest and most convenient, without a doubt, but I've broken spokes on two long rides where I did that trail and rode home (I'm in Edgewood, actually) on the trails in the park. Came out at Bartlett. I have absolutely no idea if I broke them in the park, but it's made me a little shy of it. My touring bike should be able to handle those trails--they're hardly single-track, my back wheel is a touring one so it should be basically bomb-proof, and I'm going uphill on gravel so I can't be doing more than 10-11 mph.
spokes usually break (at the elbow, anyway) due to fatigue. this can be caused by many different factors, but it is not likely due to the trauma of riding on schenley's main trials.
also: am i the only one who kind of likes going up swinburne? it's kind of the perfect combination of steep and long for climbing that hill, and i have never had an issue with automobile traffic.
also also: am i the only one that goes up joncaire on the cobbles?
like everyone else, i vary my route. i live in shadyside, and so bates is surely the fastest and most direct, but it's also the least travelled by me, because, well, it sucks. and i don't like riding on sidewalks. i rather like swinburne, but others seem to have different experiences. junction hollow to joncaire, or up neville, or through cmu are all fun alternatives. greenfield is tolerable to me, for the reasons pointed out earlier. also, you can take the road across from the swinburne bridge, which will take you up some funsteep (that's a word, right?) hills up into greenfield, where you will have the roads all to yourself, and can ride essentially parallel to greenfield ave.