It sounds like you're doing all the right things. I'm thinking that your smaller crate/expen set up will help a lot. If you keep him inside the expen overnight, at least you won't have to wake up at 3am to take him outside anymore! I know that the potty pad thing doesnt work for everyone. I had large dogs prior to getting my first Yorkie. It took a while for me to get used to having a pet go to the bathroom inside my house. But it's really not bad at all. In fact, it takes a lot of responsibilty off of me.
I got my last puppy in August. She was 14 weeks old & still was learning how to control her bladder. She would be eating & then all of a sudden, step away from her food bowl & pee! It took me a while to realize that she was still learning & that at 3 pounds, her bladder was tiny. Add that to the fact that she was born in a mill, adopted by a family that decided they didn't want her, and then returned to the rescue. That's a lot of transition for a 14 week old puppy.
If you're dead set on having Rex go outside to potty, maybe you can try rewarding him with high value treats after he goes. That's assuming you can get him to go. Classic crate training should help...keeping him in his smaller crate unless he's eating or going potty...with a little supervised play time. I kept my puppies tethered to me when we were potty training so that I could learn their signs of when they had to go. I also kept them in a plastic travel crate with a handle, so I could carry them with me & not miss a potty signal. Then I'd take them to their potty area right away & reward them with an extra special treat & praise them like they'd just won the lottery. If they didn't go after 10 minutes, I'd put them back in the crate. I know that's a lot of commitment. But it really did help me.
It also helps to take a used potty pad & smear the wet part on some grass. Lead him to that area so he can smell his scent. You can also put a little piece of his poo outside & do the same thing. You can apply the same concept to a potty pad inside his expen. And make sure to scrub down his crate & bed linens with an enzyme cleaner like Nature's Miracle, so he doesn't get confused.
The ASPCA has a great "virtual behaviorist" section & a great weekend crate training guide that might help.
ASPCA | House Training Your Puppy
I honestly have had a more difficult time potty training my Yorkies than I did my own son. So I feel your pain. But I'm hoping that some of those tips will help. Good luck!!!