Welcome Conor!! How sweet of your girlfriend and you to give him a loving home!!
Well, this could be two different things, or a combination:
1. Like you said, adapting to a new territory – Many bunnies will mark up the place to send a message to all those that may intrude that this is his domain and this is his family. If the place you moved into had animals before, he may be more likely to mark with even more fervor.
2. I am assuming he’s not neutered. Most males reach sexual maturity around 3 months, and then after that you start really seeing the behaviors you’re talking about. Has he been getting "extra friendly" lately as well? Though this behavior would have most likely shown itself earlier than this, maybe with the move, it really put it in overdrive…..so that is why this could also be a combination.
SOLUTION IDEAS:
I think you will have to re-littertrain him,(check out the litter training section on this site) but if he’s not neutered, now that this has started, it may be more challenging (It actually is amazing that he was litter trained so young – you were lucky!)
I would seek out a rabbit savvy vet and make an appointment to neuter.
And for now, during retraining, limit his freedom. Do you have an x-pen? Those are great for allowing exercises while limiting freedom. They are also easy to clean. Just be sure he has a hidey box and has several litterboxes – so that all the areas/corners he chooses to pee in are covered. Another good thing about x-pens is you can gradually allow freedom with them by expanding, yet blocking off areas or rooms.
Another member said she used the method of spreading her bunny’s scent around the house by taking a lightly damp cloth, rubbing it all over her bunny and then rubbing it over the area her bunny likes to mark. I have seen this on pet advice shows for cats, but I have not known enough people that do this with their bunny. But if it works for a cat, maybe it would work for a bunny. I know one person who said this worked.
If you have rugs, you may have to shampoo them to get the scent of the other pet out?(IF there was another pet)