Everybody has a free opinion, worth the price, but here’s mine as an owner and user of both. They would both be fine, and the downsides you mention are more theoretical internet chatter than real obstacles, imo.
The 50/2 Sonnar is sharper than the Summar, and yields a nicer result, imo. Lenses were the one biggest advantage Contax had, in the referenced time period. But, it’s a personal preference.
Trimming leaders is both easy, really easy, and takes only a few seconds. Then you’ve got 36 more frames to shoot. If that’s a problem, it’s one beyond my understanding. Has always sounded more like a feeble whine for help.
Slow shutter speeds on the Contax II being problematic in real life on a working camera, that’s news to me. Both these cameras work without issue if they have been maintained, and neither one works if they haven’t, so nothing to choose from there.
Servicing might be an issue if trying to get it done locally. Best to get one that’s recently had it done, and done correctly, than buy one and find out it had been cheerfully misrepresented by the seller. Been there. Either camera, if it’s in good shape, should stay that way for a long time.
Good luck, and have fun, no matter what you decide.