I think that sounds a good idea.
I very much doubt you are being a wuss. As I said, I had a similarly mean mw with DD1. She told me I had a low pain threshold when I was writhing in agony on the bed. When I had DD2 without any pain relief and DS with only gas and air I seriously wondered if it was too late to track her down and shout in her face that she was wrong and that none of it hurt as much as that 'not established' labour
.
The pain of being in a position which your body is screaming at you not to be in, and the pain in your back, is very different from your average labour pain, I have found. DD2 was also back to back and I'm not going to lie, it was agony. But my body told me to do X and Y and I did it, and the pain felt productive. Not less, but like I was working with it to get somewhere. The pain of being on my back being monitored felt helpless, and scary.
And you know what, I want to ban the whole low pain threshold/wuss/tough thing in labour. Because pain is what you are feeling. Even if you were the biggest wimp in the world (which I'm sure you are not), the way to help you would be to be sympathetic, give extra support, listen to requests for pain relief and explain gently if there was a genuine reason it wasn't possible. Not be dismissive of the pain.
I did a lot of stuff with my doula on processing my first birth. I suspect that things you could do to process yours might help too. 