I'm putting a half bath in a 5x9 well-insulated room over an inaccessible (from below) crawl space. I plan on a 220-volt in-the-wall electric heater and possibly a limited area of under-tile heat in the floor. But I'd also like to add a little heat from my forced-air furnace system to help reduce the cost of all-electric heat. For reasons I won't belabor here, I only have 4-3/4 inches under the floor to run a forced-air duct, so nothing bigger than a round 4-inch will work (including 6-inch oval). The duct would come directly off the furnace plenum and involve a total of about 12 feet (2 feet plus 6 feet plus 4 feet) of straight run and three 90-degree turns to get from the furnace, around a stair stringer and up through the floor. I know this is not an ideal setup, but is it worth even trying? Maybe even with a duct-boost fan? (Return air is not an issue, nor are codes.) I appreciate any insight you may offer (unless it's to consult an HVAC engineer -- unfortunately, that's not in the budget). Thanks.