Chloe Your birth story sounds very similar to my first. Baby was back to back, had big head, had pethidine etc.
I didn't have an epidural and was able to move into positions that increased the chances of him moving and he DID move during labour and came out the right way (contractions in a good position can help to turn the baby).
BUT, the barbaric hospital that I gave birth in let me scream for an epidural for 6 hours (full, short-staffed labour ward) until it was just too late to have one. As you predicted for yourself, I had NO energy left to push the baby out and after 3 hours on my back had an assisted delivery. Baby also arrived sleepy and I had problems feeding initially.
However, I have since learned and proven to myself (through birth no.2) that I don't need energy to push if I am in a good position, and that pethidine does feck all for the pain.
I planned very carefully to enable myself NOT TO WANT an epidural the second time given that begging for one didn't get me one the first time, and would urge other people to do the same.
I THOUGHT I was well informed the first time, having attended NCT, read etc. but compared to what I know now I knew feck all. I have ishoos about this and truly believe that many many women go into labour not knowing half of what they think they know and even refusal of medical intervention on half-knowledge can have potentially devistating affects.
So, I propose properly staffed maternity units, decent and informative antenatal care, one midwife to one woman and a lot of patience!