With regret, I am (for now) admitting defeat on the DDoS front, and we will soon be using using Cloudflare to protect against DDoS attacks. This change is in progress, and will take ~24 hours for everyone to see.

I really don't believe in willingly putting a man-in-the-middle in your HTTPS like this, but my homebrew DDoS mitigation has been one of my biggest time sinks for the last 6 months or so, and the necessary servers are still pretty expensive. If I had more manpower, then I would prioritize maintaining our own DDoS protection, but with me as the only sysadmin and current-software developer, it's become unsustainable.

I especially dislike Cloudflare, which I'm almost certain is basically owned by US intelligence agencies. I considered several alternatives to Cloudflare, but the smaller ones (eg. Stackpath and OVH) didn't strike me as reputable/competent enough, and the enterprise-targeted ones like Incapsula and Akamai are around $3500/month. Even though $3500/month seems absolutely ridiculous to me, I was seriously considering Incapsula due to its pretty good reputation, but then they were having all sorts of technical issues while I was trying to set it up. So I gave up for now and went with Cloudflare.

The Internet is seriously flawed if everyone needs to huddle behind these huge centralized anti-DDoS companies in order to survive...

The security implications are that Cloudflare can read everything you send to or receive from the server, including your cleartext password and any PMs you send or look at. They can't access the database arbitrarily, though: they can only see data that passes over the Internet.

Tor users and benevolent-bot operators: please wait a couple of days for the current DDoS to subside, and then post your complaints here. I am able and willing to tune Cloudflare to be minimally annoying. Not every Cloudflare site has to do that "Using Tor? Here's an impossible captcha" thing.