Oh my...poor little guy. He sounds so scared when you leave him all alone..
It's too bad that the crate won't work on him - it sounds like the anxiety has taken over the normal desire to keep his sleeping area clean.
Hmm..if I were in yours shoes, I'd use the x-pen as others have suggested so that the pee/poo is contained in a smaller area. And I agree to put a puppy diaper on him as well so the clean-up is less difficult for you. But before you start with the x-pen....
Couple nosy questions: how is he when you're around? Is he relaxed? Or still freaking out? Does he start crying/whining/barking as soon as he knows you're leaving or only after you leave? Or is he quiet but just pees/poops everywhere?
Though it sounds like you have quite a lot on your hand with a baby, I would think it's worthwhile to try to
fix the anxiety issue instead of just putting on a band-aid. I don't know how long I could tolerate cleaning up pee/poop everywhere on a daily basis
If you're able to find the time each day, even just 10-15 minutes a day, try conditioning him to learn to love being in the x-pen (ie. try to not have him associate x-pen as something bad and then turning into a place where he freaks out and wants to pee/poop). Make him LOVE this safe place. AND that you're always going to come back
So.....I'm not sure what your schedule is like, because this obviously won't work if you need to work or go out everyday...
But IF you have the time, this is what I would personally try on a daily basis to positively reinforce his love of the x-pen:
1. put him in the x-pen, play with him make happy noises with your best minnie-mouse voice, play with him with his toys for like 10 minutes, and then walk out of the room for 10 minutes. Even better would be to pretend to leave your house and close the front/garage door (ie fake being "gone"). *Pray he won't pee/poop in 10 minutes with you gone. If he does...then try just 5 minutes.
2. then come back, "SURPRISE!! Mommy's back!! Wooohoooo everything is A-okay!! Parrrrrty time! Wooooooohooo~~~~" And give him some yummy treats.
3. then, be in the room and do your usual stuff for a bit, but ignore him. If he makes crying noises, try to ignore him for a bit. Only once he quiets down, go back to him. I think it'd be good for him to relax in his x-pen while you're around and not freak out. Repeat Step 1 and 2.
4. Finished for now with the x-pen! Let him out of the x-pen and then do your usual stuff, let him roam, follow you around or whatever.
I'd say do this once or twice a day (morning and evening?) for a few weeks. They're really smart and eventually he'll learn that you're actually not gone that long and you WILL come back!
For the first few days be "gone" for 10 minutes. Then the next few days, increase your "gone" time to 15 or 20 minutes (hopefully he won't poop with you being gone for that long). Then increase it to 1 hour (or whatever you're comfortable with) and so on. OH! And since you have a baby, you must have a baby monitor - hehe you can watch him while you're away! Gradually increase to a couple hours, so you can actually go out and buy groceries or run errands. And then before you know it, hopefully, he'll be okay to be left along for more than a couple of hours. Just make sure you treat him every time you're back so that he learns that waiting patiently at home, means eventually you come home AND he gets yummy treats!
In addition to the above steps, I would also try to feed all his meals in his x-pen so that it's ingrained in his mind that this x-pen is an AMAZING place to be.
I know it's much easier said than done. You'll really have to be
very consistent to do this every day and be
super patient. Anyway, this is just what I'd do. If you manage to try it out, I really hope it works out!!