I would simply get male doggie wraps. My boss and I use them for our breeding boys who mark everywhere. You put a womans pad in it, and change often. Take them off when he goes outside.
If it is true marking, a spray bottle can also work well. Simply put water in it, and when he marks, spray and say "no".
It is possible that once he gets his scent around he will just stop. I have rescue poodle who does that. She would mark every room, and then done. I just then get my carpet cleaner out and take care of the areas.
Is he neutered? Sometimes that helps curb their need to mark. There are a few things you can do to decrease the amount of marking he does.
Besdies neutering (which is not a cure, but can help) also use a belly band on him when he is loose in the house. This will help from his odor getting everywhere.
If he does mark...use an enzymatic cleaner. This removes the phermones/scent from the urine so they cannot smell the old spot and therefore wont a tempting spot for next time.
Keep a can with pennies in it at hand, whenever he begins to mark (even when the belly band is on) shake the can...this most times is enough to startle them and get their attention so you have time to correct the behavior.....tell him NO and immediayely carry him outside yo go. If he does go outside...praise, praise, praise.
He may never be 100% housebroke now that he is already a marker, but you can reduce the amount that he does do it.