I see rifles for sale that are  Harrington & Richardson 1873 Trapdoor .45-70s. Some are called officers models and some cavalry models. I see ones says 1871 -1971 100 Yr. Commemorative of this model. Are these good shooters? They are mostly running in the $1200 to $1500 range. I am assuming that you’d want to stick to lower power loads.

I had one of the H&R Officer's models. It was a great looking rifle and an excellent shooter. Mine had the "auto eject" problem with the latch. Upon firing, the trapdoor would fly open and the empty case would come flying out. H&R took some shortcuts and did not copy the original latch design. If and when the set screw comes loose, the action will open on firing. It can obviously be fixed. Unfortunately, original parts do NOT interchange. 
Mine was a great rifle and I was very happy with it, but be aware of the problem with the latch. 
Joe S

One advantage to shooting original trapdoors is that with a few exceptions, parts are interchangeable and plentiful. Exceptions that come to mind are : 1) stocks, need the wide stock for SN over 100,000,2) sears: the three position tumbler and the two position tumbler require different sears, 3) Cadet models: stocks and buttplates vary considerably

Joe S

If you put loctite on the set screw would that work to solve the problem of the action opening upon firing?

The H&R reproduction of the trapdoor used a redesigned cam locking mechanism. Instead of a cam integral with the lever shaft, they secured a separate cam, to the shaft, by a set screw. If the set screw becomes loose, it may lead to the cam not being fully engaged, which in turn can cause the auto eject problem.
Loctite will secure the set screw and keep it from coming loose but since it is pressing on a round shaft, even slight wear, can cause the cam to slip and prevent full cam lockup.
Pedersoli solved this problem on their trapdoor by creating a square hole in the cam, which fits over a square area on the shaft. Their set screw simply allows the shaft to move in and out. Pedersoli does list their locking mechanism as a replacement part but I don't know if it will fit the H&R action without modification.
In addition to checking that the cam set screw is tight on the H&R trapdoor, a flat milled on the round shaft, at the set screw location, has been recommended to allow the set screw to more securely hold the shaft and decrease the chance of the cam changing position.
I recently acquired an H&R trapdoor and on examination found that someone had added a long set screw and drilled a hole in the shaft to accept the end of the set screw. This should keep the cam in position, although it is possible that the small set screw could shear and need to be replaced.
So it's good advice to check the set screw, if you are shooting a H&R trapdoor.
Otto