First, have him help clean up the mess in any way possible. He’s already got the stuff all over his hands, so it’s not like you’d need to worry about him getting messy. As he helps you clean up, explain that his poop has potty germs in it that can make him and his family sick, it makes his room stinky, and ruins his things. If he gets the poop on any toys or stuffed animals, don’t clean them up and give them right back. Keep them for a while. When you go to clean him up, don’t make it fun. No tub toys when you’re covered in poo because the tub toys might get poo on them. He’ll respond to the discipline best if it fits the crime. If the clean-up is too much fun, it will reinforce the behavior. If you have a shower with a hand-held sprayer, use that to clean him up instead of the tub (but please don’t make the water cold, haha). There’s less to play with and some little kids find it less pleasant than a bath.
Unless he’s extremely large for a two year old, there will be onesies that fit him. Like @augustlan suggested, you could also try a one-piece sleeper with the feet cut off, put on backwards so he can’t unzip it.
I’d also suggest trying to get to him as soon as he wakes up, before he has time to get creative with the contents of his diaper. If you don’t still have a baby monitor, pick up an inexpensive one so you can hear him start to stir and go into his room right away. Give him extra hugs and attention for having a clean room.
Finally, since he’s so regular with his bowel movements you might want to consider having him sit on the potty as soon as he wakes up. Even if the first few times he goes poop on the potty it’s pure luck, you’ll be reinforcing the idea that poop belongs in the toilet.
Giving him play-dough is an excellent idea. You can even look up “recipes” online for making your own play-dough or other messy, tactile things that toddlers love to play around with.
I have three kids, and while none of them ever played with their poop in this way, I have heard of quite a few who did. I worked with infants and toddlers for several years, and one thing I learned is that almost anything a little kid does falls into the range of “normal.” I wouldn’t worry about it unless the behavior continues in spite of everything you try to stop it, if it keeps happening after he’s been potty-trained, and/or other behavioral issues are present. Most likely he’s just bored and gets a sense of power over creating such a big response from Mommy and Daddy.
edited to say: I missed the comment above where you said you put the baby monitor back in his room. Sorry!