
The whole point of crateing for housetraining is to capitalise on a dogs unwillingness to soil it's bed.
This isn't working for your pup, so he either can't hold out or doesn't mind the soliling. This is not a good habit for him to get into.
I would not crate him at all, but leave the door open, unless of course he might get into trouble by being loose in the room the crae is in.
If that is the case I would attach a puppy pen to his open crate so he has an area away from his bed to toilet in, and continue with the toilet trainng in the day. If you have the stamina for it I woudl get up every few hours in the night to take him out so that he does not get a chance to toilet.
Personally I have never been that diligetn and just cleared up night time accidents and by being consistent in taking them out in the day they housetrained fine.
This means after waking playing eating, and every time they even looked liek sniffing or squatting!!! and every hour while awake.