I'm a tad on the heavy side and had a Brooks Flyer (sprung) that tended to break nose bolts (one a year on average) and ultimately had a broken frame. I have not had the same issues with the replacement unsprung B66 Brooks saddle which replaced the (stolen) Flyer. I think the constant flexing of the Flyer's spring created my breakage problems. There was also a bit of a sense that the Flyer would launch you like a cartoon character if you hit a good bump.

Cheap suspension seatposts seem somewhat useless, make it hard to accurately set the seat height and are absolutely useless if your weight compresses them significantly. I've never used a Thudbuster but they seem to be a seriously engineered product that looks like it would smooth out the ride. Can't speculate if this would help your back problem or be any better that bigger softer tires.