This topic got bumped up for me now, so here’s some sort of an answer.
Coda API and cross-doc stops working when the doc’s JSON goes over 125 MB limit. You can see the limit in developer tools — that would be the largest file loading. Usually it’s much smaller though in compressed state — 125 MB is the limit of uncompressed one.
Got this info from Coda support. That said, the doc would still load in UI even if it’s over that limit.