Microsoft SQL Server MERGE deadlock issue
I think what you are talking about is not "deadlock issue", it's not even blocking issue.

Full backup locks nothing, but when it happens you have intesive I/O operations, it's just increasing server load. Full backup should be done with the less possible activity on the server, but your activity is not even readonly, it's data modification. If your db is in simple recovery model, making merge during full backup means fully logging, so you have more writelog on inserts.

Update statistics really can deadlock with merge when it reads indexes in opposite order, I saw the cases. But it's surely not your case:


  The system task Deadlock Monitor wakes up every five seconds and
  checks if there  are any deadlocks in the system. When a deadlock is
  detected, SQL Server rolls back one  of the transactions with the
  error 1205. That releases all locks held in that transaction  and
  allows the other sessions to continue.


Expert SQL Server Transactions and Locking: Concurrency Internals for SQL Server Practitioners
By Dmitri Korotkevitch

So when you say that your task completes in 10 minutes it's definitely not a case of a deadlock: even if it could be UPDATE STATISTICS to be rollbacked, it happened in some seconds, then it was killed and your merge continued as usual.

To find out the exact cause of slowness you should monitor sys.dm_os_waiting_tasks during the execution to detect for what your merge is waiting for.