Hi Jarrad, welcome to Outdoorking. Having the reel run out of meat for resharpening is something that happens to all cylinder mower users eventually. As you will have noticed, a new reel is typically more expensive than a second hand SB that has a decent reel. There are two alternatives to a new reel. One is to have the blades replaced on your old reel, and the other is to buy a beaten-up, non-running SB that has never been resharpened, and take its reel plus many other parts for spares. At least in the Eastern states, the latter is usually a much better deal: the majority of SBs are never resharpened, and many of them have been parked in garden sheds for decades without being used. Several Outdoorking members buy these rusty wrecks and restore them for resale.
Replacement of the blades is possible, and is done fairly regularly by specialised engineering companies. I've never heard of it being done satisfactorily by an amateur. The blades are made from a fairly high carbon steel, but it is not in a fully hard state: reels can be resharpened by lathe-turning, which is not something I'd attempt if they were spring-hard.
Without knowing your skills or physical equipment, I doubt the practicality of replacing your blades yourself. A toolmaker with a lot of time to waste could no doubt do it (or just about anything else: toolmakers' skills are awesome), but I do not think it would be worth his or her time.
