The first thing I suspect is that the guide pulley (the top one) is hanging up on that biggest cog. If there's not enough "B" gap (space between large cog and guide pulley) to let the chain lift off the cog's teeth during a shift the chain will act as a sandwich or splint trapping the two together.

The first ways to avoid this is with components that are meant to work together. Like a rear der whose large cog capacity is the same or greater that the large cog of the set. sounds like this isn't the case... is it?

A few points-
When shortening the chain make sure you can still shift into the big/big cog/ring combo. Serious damage can happen if the chain was found to be too short and you forgot to not shift into the big/big.
A long cage rear der might not have a claimed largest rear cog size greater than it's short cage sibling. Shimano road ders on the early/mid 1990s, when they offered SS or GS cage lengths of their 105, 600 and DA models, had the same 27 tooth max cog limit. The long cage only increased the chain wrap/take up spec.
When exceeding the chain wrap capacity, it's usually "safer" to have a slightly too long chain that droops on the small/small combo than a too short chain.
Make sure any der pivot springs are working. Some ders have both the B and the A (B is the hanger axis pivot and A the cage's) sprung, some only the A pivot is sprung.
If only tiny amounts of B gap are needed more one might see if the guide pulley could be replaced with a smaller diameter version. Andy