First thing you need to do is take the shirt out of the carrier. Don't put any blankets, towels, shirts or anything of the sort in the carrier. Make sure that it is bare. It might seen harsh but having these things in the crate can actually encourage him to go to the bathroom in his crate beause he knows that he can go to the bathroom on the shirt which will absorb most of the moisture and then all he has to do is push the shirt out of the way. Dogs don't like laying in their own pee and poo and by having a shirt or blanket in the crate he can still go potty in the crate without having to lay in it. I have noticed this in many puppies and dogs, once you take away the towel they won't go in it anymore.
Also, make sure the crate is small enough. If he can go to the bathroom and one part of the crate and lay down in another part of the crate, then the crate is too big.
Switching training methods right now can really confuse him. Just stick with him going outside. When you take him outside and he goes, reward and praise him and as an extra bonus either take him for a short walk right afterwards or let him have his playtime. Only give him 10 to 15 minutes to go potty outside, any longer and he will forget what he is out there for and it will defeat the purpose of house breaking him. If he does not go, put him back in the crate and try again in 10 minutes. This will help him learn that if he goes he gets out of his crate to play or go for a walk and if he does not go, he goes back into the crate. Remember to give him a command each time you take him out, such as "go potty" or something similiar.
Don't worry he will get the hang of it, it just takes time and consistency.
