Apologies for not getting back to this sooner. We have a solution, after many hours of working with JTAC.
We had 2 bugs that were biting us:
1) PR1321612 (against 15.1X53-D57) for the first 24 ports (on a 48 port unit) act like a hub and flood unicast traffic in the VLAN, traffic ingested by the upper half has the same problem, but traffic egresses in the upper half normally.
2) PR1326857 (against 15.1X53-D56) for packet duplication - each switch doubles some of the packets that are coming in/transiting. Some cases a client would send 1 dhcp request packet, and would get 4096 replies (all the same transaction id, verified that the server didn't send that many, etc) - the more switches you chain together, the more amplified the problem becomes.
We're currently running D55 and things have been stable for a couple days.