I've got all 1968 turns of wire on the bobbin, and there's plenty of room for the heater windings! I should know soon if it works. It wasn't that bad winding it, just time consuming (about 20 minutes per layer). Neatness was crucial. I sprayed each layer of windings with insulating varnish to hold things in place, and add some insulation, and then covered it with a layer of Kapton tape.
I can see why power transformer rewinding is expensive. First there's disassembly, and reverse engineering, which wasn't that hard since this one hadn't suffered a severe meltdown. The materials cost is quite high. I spent about $60 on magnet wire, and Kapton tape alone. I already had a spray can of insulating varnish, and one of the magnet wire sizes on hand, so I'm not counting those costs.