The gut slowdown could be from bonding-stress, so it doesn’t have to be that he ate sth he shouldn’t have.
Hay is of course great, hay and water. Hydration is important. You can give ranitidine to a rabbit (Zantac), it acts as a motility drug. I’ve given 1/10 of a 150 mg pill for humans to my rabbit Yohio as per my vets suggestion when he had gut issues in Nov 2014. (I divided a pill in 4ths, then a 4th into halves and then took of an itty bitty bit of that tiny piece and crushed the rest between the blades of two spoons, mixed with water and fed by syringe. The risk of overdosing is low according to this, scroll down to “Overdosage”: http://www.drugs.com/pro/ranitidine.html
I only gave the dose once per 24 hours but it seems you can give it twice: http://wabbitwiki.com/wiki/Common_drug_dosages_for_rabbits
On ranitidine’s usefulness for rabbits:
https://www.vetstream.com/lapis/Content/Generic/gen00848.asp
That’s all I can think of that’s possible to do at home. Very, very light tummy rubs might help too, but very light. With my Yohio, the ranitidine set his bowels into motion after like 20 minutes, but I don’t know if that’s normal for all buns.