If you can find a blackpowder/cast bullet loading that will shoot 2 MOA or better out to 500 meters, your rifle or carbine will at least get you started in BPCR silhouette.  Generally, the .45-70 is eminently capable of such accuracy in a good gun.

As ssdave has pointed out, the chief handicap after that is the lack of a finely adjustable sight.  You might see if MVA could adapt one of their staffs to your H&R base.  You get sighters at Silhouette matches, and they’re generally over in a few hours, so if your sight base is tight in the wood, it alone shouldn’t be an impossible handicap.  You’re not routinely lying out there for days in alternate pouring rain and baking heat, swelling and shrinking the wood.

Gong shoots frequently have a special “Trapdoor class,” where unmodified originals, with Buffington sights, can often get uncomfortably close to those with more specialized equipment.  The first time I went to the Quigley, there was a guy who shot the whole course, offhand, with a Trapdoor army rifle.  He got the same score as me, a 21.

For a first approximation, though, taking your Officers’ Model to a local shoot and seeing how it goes, will at least inform you of the issues in play and let you decide what you might want to do about them.  There are sometimes even rifles and accessories for sale at such affairs, that can help get you further into the game at a discount.

Lee Shaver will adapt one of his Soule style rear sights to your H&R Officer's Model. Best to send the base to him for a positive fit.  I have done this and makes the rifle much more adaptable for shooting at different ranges.
For an upgrade, I would recommend looking at a CPA Stevens. Probably the best value for the money. Has the capability to interchange barrels easily. Mine has both centerfire and rimfire barrels.  They are made to order so you can spec it just for you.
Mike.

Thank you to all that replied. Great information to research. I really do appreciate the help....

Thanks Ranch, great information. I love my officer model but worry about the stock. I had to have it repaired as I dropped it and a piece broke off. I had a shop repair it and it looks great, just wonder if the barreled action would fit in another style stock so I can have confidence and learn the sport. I could not find a replacement. I also agree with trying a few shoots to learn.

Check the Shiloh Sharps Rifle forum and do a search on 'trapdoor' (don't recall if the threads were in Shooter-to-Shooter or Black Powder). There are a couple of good threads over there by Woody & a couple of the better TD shooters (at least they hold many of the national records with same) that discuss loading and shooting the TD out to 600yd with the Buffington sight, including details about how they adjust the sight accurately. Includes pic's showing the tools they use for their adjustments. While it takes some effort, Woody, John Bly and a couple of other TD shooters can put some respectable scores with their TDs.

In my humble opinion, you're on the right track with a high wall. I had a really nice TD with a buffington sight, but the front sight was a mere speck, so I moved it on. Luckily I found a like new Ballard Arms Co. high wall in 40-65. Came with tang sights and interchangeable front sight. Bore is mint and has a single set trigger as well. I think I did pretty well in the deal, hopefully you can be as fortunate in your search as well. I congratulate your good sense in moving beyond the TD, as the care and feeding of an original TD can be a challenge. Having said that be aware that any black powder cartridge rifle shooting for accuracy is a challenge. Which is why you're here, right? Good luck in finding the right high wall for you.