The ceiling beams are boarded out and plaster boarded, then there's a metal lintel about a foot high. Then the wood door frame.
Its standard practice to move the door frame in to give the door a straight run down. There by also giving opportunity to raise the roll as high as possible as the run to the runners is straighter and less likely to buckle, of course. This means minimal door can be left in the runners.
On first glance, 15" is plenty, it should then clear the door frame, where the current door hangs a good 6" lower than the door frame depending on where you position it. Even if the roller also hangs 6" lower giving 21" of depth as the current door, that's still a vast improvement on the current doors 6ft square head banging, plus I can hang stuff on the walls right near the door.

I'd be surprised if the roller was lower, I don't see an issue but a roller is the way for space. That just leaves cost.