Is it safe to move big table to another tablespace while working with it?
The table will be AccessExclusive locked for the duration of its move to a new tablespace, so your application will seize up during that time.

You haven't really described what your workload is, so it is hard to recommend settings to accommodate it.  Surely it wasn't 15 separate one row inserts and ~7 select operations per minute which lead to the existing bloat?

Generally it is best to delete rows once you become aware that they are eligible for deletion.  Creating a deletion-queue table is just another table which can get bloated, needs to be maintained, have deletions done on it itself, be vacuumed, have code written to accommodate it, etc.