I was just playing a Menagerie Preview game against a bot. The game ID is 36468748.
On my last turn, I played many Throne Rooms and many Kilns. At various points in the turn, the game froze for a long time. I didn't check a clock, but it was easily 10 or 15 seconds each. At one point I switched to another browser window for a while, and when I switched back it was still frozen.
I don't know for sure, but I suspect the game might be having trouble handling multiple stacked Kiln and Throne Room triggers.
Thanks for the report, Qaanol!
I'll put your report into the list of things to check. Also big thanks for mentioning the game number, as that makes it much easier to reproduce the problem.