I don't have a ton of useful tips ... mainly just empathy. My little girl was the same way ... she only slept on my chest for the first three months of her life! At about three months I was able to lay down with her on my chest still, then *slowly* roll her over to her back ... the key is *slowly* and then keep a heavy hand on her for a few minutes while I slowly move it away (too fast and the sudden loss of my body heat woke her up ... I still do this with her). Starting at 4 months she now prefers laying next to me to sleep rather than on my chest.
What also worked for me is nursing her to sleep lying down, then doing the same thing as above when she's deeply asleep. (We co-sleep though, and I always lay next to her when she sleeps).
This source talks about the same nurse to sleep technique:
Nursing to Sleep and Other Comfort Nursing
"... You can also work on slipping away after baby goes to sleep. Make sure baby is *deeply* asleep and no longer swallowing before you try this (you may have to wait a while). He'll then be doing what we sometimes call "flutter sucking" or comfort sucking, a really light suck. When a baby is in a light sleep, you'll see facial grimaces, partially clenched fists, muscle twitches, fluttering eyelids, and overall tense muscle tone. You can recognize deep sleep by an almost motionless face, regular breathing, still eyelids, and especially the limp-limb sign -- arms dangling weightlessly at baby's sides, hands open and muscles relaxed.
Once baby is in a deep sleep, try and slip away very slowly. One thing that sometimes helps is to slip a finger in baby's mouth near the nipple, then ease the nipple out so baby is just sucking your finger. Then you can ease your finger out of his mouth - it helps to put a little pressure on baby's bottom lip as you do this. By doing this, you can often keep baby from waking. Putting something right up next to him that has mom's scent (a t-shirt, pillow, or an animal he sleeps with) also helps.
My kids often seem to detect the loss of body contact and warmth when I get up. As I'm getting up, I keep my hand(s) on baby for a few moments, then *gradually* take them away so the transition isn't so sudden. Baby will usually stir when I get up, but often goes back to sleep if I keep my hands on him till he gets still again. It can also be helpful to put a hard pillow (preferably a warm one that you've been sleeping near) beside baby in the spot where you were sleeping so that he doesn't feel empty space if he reaches out in his sleep. If baby was resting his feet on me (common with mine), then I'll sometimes even put a pillow under his feet. With an older baby/toddler, I lay him down on top of my pillow if I'm trying to put him down on the bed when he's already asleep. (Keep in mind that it's not safe to use pillows with young babies due to SIDS risk.)
It's often easier to slip away during a nap when you're both lying down. If you're nursing sitting up, the position change may be waking him - you might try nursing him on a pillow in your lap so you can just transfer him to a bed or the floor without moving him around as much. If baby wakes when you put him in his crib, you might try moving him to a pallet on the floor or your bed, instead of his crib - he might nap better in a different place."