All my kids (3) have a heartbeat bear - it has a thing inside it that you turn on and it sounds like your heart while the baby is inutero. I got the ones from Dex - they are $20. Sound shuts off after 40 or 45 minutes. But the sound "box" can be removed later for the kids to use him just as a teddy bear.
And, now I'll be controversial. I have an 8 year old, a 3 year old and one that is just under a month. All my kids were pretty good sleepers - but I swaddled them and put them on their tummies.
Now, I realize that you're not "supposed" to do that. But when I was a kid, babies were only supposed to be on their tummies. I'm not saying SIDS isn't a real thing - but if your baby has no health problems and the bed isn't full of "stuff" there shouldn't be a problem.
For my first, I tried to put her on her back. But she NEVER slept. And I do not do well with no sleep! So, I started putting her on her tummy for naps. Then I could check on her and make sure things were ok. After that, I moved to putting her on her tummy all the time. (First night she was on her tummy, Hubby stood over her crib watching her all night!)
And, #2 and #3 have all been put on tummies as soon as we got home. And both are great sleepers. My son (#3) slept from 11 o'clock last night until just before 7 this morning.
You might consider trying this for naps and see how he does. Then if/when you feel more comfortable with it, add nights also.
Whatever you do, I hope you figure it out - it sucks to be exhausted with a new baby!