Nap help - he won’t sleep without contact (12 weeks)

My three month old will only nap in the sling or being held. I know this is totally normal for a three month old but because I’m so injured from birth. I need some time to do my physical therapy exercises and I can’t do that with a sling on me, obviously.
Every time I put him in the pram for a walk, he just cries and raises his little arms. It’s like he doesn’t want to be on his back. Sometimes we swaddle him and rock him to sleep, but as soon as I transfer him to his Moses basket/ crib, he instantly wakes up. It’s like he’s offended to being put on his back. I’m really desperate for at least one nap of the day being off of me. What can I do?