Just a few comments to add concerning the cocking positions of the hammer which is controlled by the tumbler on the inside of the lock and also touch on your concern about the bore of the barrel. This info is from the Poyer/Riesch book which I think you already have.
The trapdoors went through 3 types of tumblers--Type 2 added the extra quarter cock notch
Type 1 only had a half cock and a full cock---used to circa serial number #28,000 for carbines and #78,500 for rifles.
Type 2 added a quarter cock notch which kept the breech latch from accidentally opening. Used after the above-listed approximate serial numbers
Type 3 had slightly deeper notches for half and quarter cock---added after serial number #275,000
According to the Poyer/Riesch book the third variation hammer (beveled lip on the hammer face) was approved in 1880 but has been seen on serial numbers as low as 86,000 which would have been mid-1878
Next would be your concern about the bore. The lands and grooves in the Trapdoor are equilateral. In other words, the lands are just as wide as the grooves. I think that the six lines you see in your barrel are not the grooves but instead are the shared sides of only three grooves and only three lands. In other words, you are only looking at a standard number of three shallow lands and grooves which create the six lines you see. I had this same issue the first time I looked down the bore of my trapdoor. I finally slugged the barrel with a .452 bullet and could then see clearly that the grooves were just as wide as the lands and only three of each. On many rifled barrels, the grooves are much narrower and thus look more like lines all by themselves. I hope that's not too confusing. The bottom line is that I think your barrel is correct.
Lastly, I noticed that your rear sight is not complete. It's missing the ladder's elevation slide which engages the graduated steps on the side rails of the sight body to raise the ladder and sight for longer ranges. Of course, you don't need it if you are not going to shoot the gun at longer ranges but then you may want to get a replacement just to make your rifle complete. I haven't seen any slides for sale but Al Frasca has both the ladder and slide assemblies for sale on his site. It appears that he may be closing out his trapdoors and parts since it appears that he is not attempting to restock anything he sells at this point so you would have to call or email him to make sure what he has.
The Trapdoor Collector
However, another online seller of parts has the same ladder/slide assemblies in good condition for only $20 plus shipping. He also has some fair/lower-grade assemblies for only $10 plus shipping. You want to make sure you get an 1873 ladder and slide since they
updated the rear sight in 1879. The new sights mounted a new rear buckhorn-style sight directly on the slide and added the ability to adjust for windage.
Granpa's parts--1873 sight ladder and slide
I bought my model 1873 Trapdoor made in 1879 from Mr. Frasca about 2 years ago along with a nice mint condition bayonet. I later bought a complete rear sight from him to mount on a NIB reproduction Officer's model trapdoor made by H & R back in the 1970s. I could never afford the $20k starting entry fee for an original Officer's model. Mr. Frasca only has one rifle for sale presently and seems to have not added any inventory in at least a year. As already mentioned, it appears that he's simply getting out of the buying and selling aspect on his website--maybe selling off due to age. I'm almost at that point myself.
I'll post some pictures of mine if you don't mind me adding them to your thread.
Cheers
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