The idea that immediately came to my mind is that given that the site is probably load-balanced, the best thing to do would be to take the site out of the load balancer while the big GC runs, then put it back in. I wonder if there's some way to hook that GC event. So, "pools", but at a higher level.
Reading that page it is clear that this is either the exact scenario that page is covering, or at the very least one of the core use cases.
It's triggering my Wrong Thing To Do senses, but, well, when the GC isn't quite right, hacking around it may be the only option.
We register for notifications from the GC using a magic threshold number that could mean anything.
Then we quickly notify the rest of the webs a GC is pending on our "message bus". They let us know they are safe from GC at the moment. If they are not you are in a pickle.
Then we notify HAProxy that we are about to run a GC and ask it to tell us when it is done draining the current requests and taking our web offline.
Once notified we perform the GC manually
Then we notify HAProxy that we are done with the GC so it can add us back to the pool.
What could possibly go wrong?