Yes switch sides every feed - this is the answer - don't stay in the same position! You just flip them over with you and then each side gets a rest. I would also sleep with baby in the crook of my arm, baby's head resting on my shoulder. Often with not much else on and duvet quite far down. They didn't overheat if they had little clothes on. Mum next to them is proven to help regulate body temperature. I remember when DS had a temperatue aged 7 months but the moment he started feeding and was in my arms, it started to drop. Just being right next to you is enough to regulate body temp.
also it sounds like a bit of daytime movement, exercise would really help. Are you managing to get some walks in during the day? I know it's so hard at the start, especially with being sleep deprived.
But a walk and some yoga and just gentle stretches to help you cope with nights might really help.
If i don't move during the day I get stiff neck and hips. OK, i'm older now but movement has always helped me in so many ways.
Swimming and sauna is amazing too, if you have time. Swimming takes all the weight off the joints and sauna is like the icing on the cake.
I also put the mattress on the floor and DH was banished for a long time.
In the end we broke the cycle at 13 months. DH took baba for 5 nights and she screamed but it was fine. She was safe and in loving arms.
I think 8 weeks is too young though. I even tried at 4 months, it didn't work. You need to wait a bit. Sorry, not the news you want to hear.
But it's so worth it. I have very well adjusted happy kids who and we are very close. I never ever regret co-sleeping. It was the best thing at the time. I wouldn't do it any differently. Not ever. I loved them so much (still do!) and like all mammals, I truly believe we are supposed to sleep together in those early months.