Granted... it would increase the cost (since you're adding reverse proxies) but it would be a quick way to get acceptable latency, rudimentary DDoS protection, and you could try different connection options independent of the main app's logic.
It would be hard to estimate how much latency you're adding with a SSH2 reverse proxy in this case, but it's probably lower than one might think.
The idea of letting Claude loose on my crypto[graphy] implementation is about the most frightening thing I've heard of in a while [though libnss is so craptastic, I can't see how it would hurt in that case.] But I loved this write-up. It was readable and explained the problem the OP was encountering and proposed solutions well.