I'm sorry to hear about your first HB experience.

Would it be an option for you to still birth at home, but get synto afterwards vs a physiological third stage and if within a short amount of time it looks to be a problem, transfer to hospital?

I can't see why the birth itself would be an issue UNLESS there is risk of a huge bleed within moments of the birth?

ETA - Just remember that GP's aren't OB specialists. Best to leave these decisions to a MW or OB. No MW would put herself in a position to risk a massive PPH if you are at risk, so I would be inclined to follow her lead vs your GP's