Can replicated commands be forced to follow each other in transactional replication?
It sounds like you'd benefit from using procedural replication for those stored procedures.  That way, SQL Server will just run the procedures on the replicated instance rather than replicating all the DELETE and INSERT operations.  I'll wager that will be much faster and will reduce latency in addition to fixing the issue you're seeing where the destination tables are empty for a period of time.