Thought that myself...
If you choose the correct powder, you can obviate the need for a filler altogether.
Or, if you are looking at reduced practice or cast bullet load, use the backer rod you just bought.
I used that with the Varget cast loads myself although I used 1/2" foam rather than anything bigger.
You may find that stuffing your cases with the foam you bought may be tedious. Please report back to us on that.
I worked on loads for a 404 I once owned and used backer rod in some and no filler in others and there was no difference that I could detect. There may have been a lower fps deviation with the filler loads but I didn't chronograph them and all shot to the same POI so it didn't seem to be much of a consideration.