Ok Melly, I have had 6 kids and never had the single shot needle.

Angel was Phys 3rd stage, all good.
Chill was Phys 3rd stage, all good.

Princess was not done properly. They took her off me, swaddled her up and then let half the family into the room. I could not feed my baby, I could not go to the toilet, there was a sheet between my DD1 and DS1 and a sight they did not need to see. I bled. >3L PPH. It was not a rapid bleed, I might point Glamourcide in here to cover that part for you. Anyway in a real PPH situation, they don't bother with the needle, you get the drip. The needle is too small a dose to properly control a PPH.

Tsunami and Hurricane were both managed to the extreme with canula and synto drip. That is because of what happened with Princess. I was an increased risk of PPH.

They wanted to do the same with Diva because I am an increased risk for PPH. I have the prior PPH risk factor and Grand Multi.
I got my phys 3rd stage with Diva. No PPH.

The second most important thing you can do for a Phys 3rd stage is tinkle.

As for the Oxytocin taking a while to work.. That is a new one on me. It is a fast acting hormone. It is also short lived so you are better off getting it when you need it. There was a study that compared giving oxytocin at the birth of the shoulders against after delivery of the placenta. They had more success in lowering blood loss and preventing PPH in the group that were administered oxytocin after the placenta was delivered.

Feed your baby, empty your bladder, snuggle as much as possible. Phys third stages are perfectly achievable, even with a history like mine.