Fire and Forget SQL Triggers?
I think I would build a table with a queue of some sorts, and have a job poll that table and pick up any work it has to perform.

So for example your trigger writes a record id in a table called processqueue, then you have a job that picks up all the records from the processqueue table and do it's heavy lifting for each and every record, removing the record from the queue once finished.

Schedule that job to run according to latency requirements