If you are too hundred yards into your backing, you have different problems, you are either solo, and you won't stop that fish, or your pal on the boat doesn't know how to drive, or you don't have room or depth to drive the boat. Either way by 150 yards, your drag needs to be at 6 lbs at least and if you can't stop the fish , you can't stop the fish. My go to Tarpon rod is a 9WT, but when I hook a 50-60 lbr you have to be aggressive with the drag and the pull. I would prioritize fitting the fly line in the reel comfortably vs stuffing it. There are other options like mentioned to fit longer backing, but take a look at how many times you have needed 200 yards w a 9wt. My guess, zero? Once?
Now my 10 and 11 WT rods have 250, a big 80 lbr plus will put your there easily. .02 cents...