Here;s an option, and one I performed on a CVA .32 and price was reasonable.
Skinner sells a tiny stem type peep sight, called the Lo-Pro. It is about the most affordable rear sight they offer. I have not priced one lately, but as I recall $30 or so. Rather than try and describe, one can search it easily. On certain T/C rifles, there is a tiny hole, plugged with a slotted screw, on the top of the hooked breech recess at the end of the tang. The threaded shaft of the Lo-Pro will fit that hole, if you buy the right diameter version. I cannot recall what size that hole is or the appropriate screw/thread size, but if your rifle has that tiny hole, ONE of those Lo-Pro sizes will just thread into it.
The Lo-Pro is aptly named, it sets LOW on the rifle, I'd speculate LOWER than the maxed down OEM blade rear in the pic. If one is willing to experiment, the OP might find his lofty shooting Hawken might come on target with the Lo-Pro. The few accounts I've read relate their rifles shoot LOW with the tiny peep and require a front sight change. That was the result of my experiment and I had to add new front on my .32 as well. Since the OP rifle shoots HIGH at present, MAYBE the Lo-Pro will do the trick. The factory blade rear will have to be removed. There is no windage adjustment on the L0-Pro, only elevation, so windage adjustment shifts to drifting the front sight 'till you get what you need.
If the factory hole is not present, a good machinist can drill and tap what you need. There is plenty of metal there. One could consult online pics to see just how the factory whole is located. That of course would add cost, but I had an acquaintance that did the job for me...... I rewarded him with a bottle of Wild Turkey!!!!!!!!! He said to bring another job anytime
I did the front sight swap myself from an online purchase. Hardest part was getting the right dovetail size to begin with. The OP may not need a new front...as I said....an experiment of sorts.
Whether or not the hole is there depends on when your rifle was produced and the model. Some of my T/C's have it, some do not. I've heard it said it was for a scope base, and I've also heard it was for a machining jig fixture.
Best of luck