I have multiple FME workflows that trigger once via my directory watch. How do I avoid a SQL deadlock since they all upload to the same SQL database table?

Set up job queues to route them all to one specific engine so there can only be one running at any one time?

Agree completely, this is probably the easiest workaround.

For a more performant solution, if necessary, have a look at your database back-end and how it supports concurrency and avoiding race conditions. For example, here are some ideas relevant to SQL Server: https://dba.stackexchange.com/a/187411