On system you describe you are correct that only vented loop you should have (many boats don’t) is on inlet for toilet (to flush head) I think. If I understand correctly your system will have 4 lines or hoses:
•¾” inlet from thru hull to head (flushing water)
•1.5” From head to Top of holding tank (toilet discharge)
•1.5” From Bottom of tank to deck fitting (pump out)
•¾” From top of tank to vent
But I’m back to thinking tank (& thus inlet) must be lower (or level) then head in this system again.