How to set ALL the replication to DEADLOCK_PRIORITY LOW?
After having a good setup and monitoring the tempdb
we opted and used the READ COMMITTED SNAPSHOT as described in the comments.
How to implement Read Committed Snapshot and how it is different to Snapshot has been nicely described (including links explaining how to set it up) here.

In addition, READ_COMMITTED_SNAPSHOT (henceforth called RCSI) will
only give you some properties of optimistic concurrency. RCSI and
Snapshot (SI) differ in three main ways:

RCSI will be used immediately by all RC isolation queries.
RCSI provides a point-in-time (snapshot) view of the database for a single statement.
SI provides a point-in-time view for an entire transaction.
SI can have write conflicts.


also quoted from the same source:

Other useful details relating some gotchas and caveats when using
RCSI/SI can be found in these articles:

Implementing Snapshot or Read Committed Snapshot Isolation in SQL Server: A Guide
Read Committed Snapshot Isolation: Writers Block Writers (RCSI)