My boy Gibson does this quite regularly. He's been to the vet and there seems to be no medical reason for it. It is exactly the same noise.
The first time he did it was around midnight on a Sunday, I was terrified, wrapped him up warm and cuddled him, was so worried we were going to lose him as it was constant and so loud. A quick cough and it stopped..!
It seems he gets this with his nuggets, though not every time, and occasionally with hay. It's like something is a little caught in his throat and a cough dislodges it.
Ask the vet to check in case there is something going on, but try not to worry too much if they don't find anything. Gibson was actually doing this this morning at 6am, but it right as rain, eating and drinking as normal.. I think some piggies are just noisy..
I hope the other issues rectify themselves quickly. I know it's probably silly, but have you an electric toothbrush you can wrap in a tea towel and slowly move along his sides/underneath him, to try and stimulate his gut?
Sending hugs x