Generally going up the mast will always be cheaper then dropping the mast.
Plus you have to assume that in dropping the mast there's a good chance that rigging will get damaged, or you'll feel the need to go ahead & replace something that is questionable. That is not such a bad thing & a wise investment to replace worn turnbuckles or mast head parts that look corroded. Most good quality bosun's chairs don't cost more then $150. or so, & the benefit is you get to keep the chair for future use. Dropping the mast is really for major maintenance items. I have been wanting to replace my aged wooden spreaders since I bought my C 30, 3 years ago. Like most sailors, when the mast comes down, its time for an overhaul. Usually that old worn aluminum mast needs to be sanded & repainted, a $500 invnestment for professional paint, etc. Replacing old halyards & adding a spinaker halyard & block, $350+, replacing wooden spreaders on a C 30: $800? more or less. Then there's the removal & reset fee & costs. That's why most of us wait on dropping the mast until we have the money, time, & the materials to do the job right, or not at all. My advice is to buy a decent bosun's chair, find someone you trust to haul you up with your mast mounted winch, & do it yourself & save money. I hate going up the mast, as any wave action movement it 10 times rockier when up 40 feet high. But the satisfaaction of doing it yourself is worth more then money saved.
ps. If your furler works, then why replace it? We had a "new" design Harken Furler that was a total piece of junk that jammed no matter how it was rigged (multiple configurations). Don't fix it if its not broke. Put your money into replacement items that are necessary. My 2 c.