I would look first to the state of the sql server running the bts management dbs. Enough room, db and indexes in good shape? etc. Then I would look to the throttling parameters. I believe your sql engine is under powered, or overly constrained in some way.
try simplifying the system to find the bottle neck. Is the ws that handles the sql inserts handling its deadlocks appropriately? can you convert to use bts sql adapter to test?