Even more evidence:
Recently moved the bot off my server (with the 2-hops over CenturyLink) to the server/site it's supposed to operate on in Germany... Since I did that, zero timeout errors to Twitter.
Only problem is that for some dumb reason 1&1/ionos don't have traceroute installed on that box. This isn't the stupidest thing they've ever done (they use X-Forward IPs as the incoming IP, so you can't filter non-Cloudflare IPs, causing me big headaches), but it keeps me from seeing what path is actually being taken.