I have a Hepburn chambered in 40/60 Maynard. This rifle shoots two good groups at 100 yds but 2 inches apart. There doesn't seem to be any pattern to which shot will go in which group. 
I shoot from a sandbag/cross sticks directly on the barrel just ahead of the fore end. The situation repeats with irons and a scope.
The two group remains with the fore end removed.
The hammer sometimes will rebound to the half cock used to clear the firing pin. It does not do this every time. 
The crown shows a uniform grease pattern.

Does anyone have any ideas?

I don't think it is the load. Here is the load just in case.
19gr 5744 Fed210 2.846 oal
.035 card wad with 1.3gr poly fill
422gr grease groove sized to .409
30 inch bbl 7 groove 16" twist .407 groove dia .399 bore dia

The buttstock has no wiggle that I can feel. 
The groups are diagonal to each other. Second group is at 10:00 to the first group. Both groups are round.  This is staying consistent.
I will try resting 3" from the muzzle.

If you've shot this enough times to know that the two group phenomena is repeatable, (not just a 2 or 3 or 4 time coincidence) then I'd increase or decrease my load by .5 grain, to see if you're right on the cusp of a harmonic, and the load velocity variation is causing the barrel to vibrate differently.  Moving the velocity away from that harmonic will sometimes change the grouping, if that's the culprit.  If moving the load that much changes the grouping dynamic, then shoot loads at .1 grain increments to find out what works, and what doesn't.

Moving the resting point does the same thing a different way.  It should affect the barrel harmonic, and maybe move you away from the harmonic node at your velocity if that is causing the odd grouping.  Needless to say, try the two things independently of each other.

I'll be burned for this heresy, but I do not like the use of 5744, I think it is too inconsistent and has too sharp a pressure curve, being double base.  I'd speculate your vertical stringing is because of wide velocity variations due to that steep pressure curve.

I'd try substituting H or IMR 4198; they have very similar burn rates to 5744 but the 4198 is a lot more predictable,  and has a lot less velocity variations.  It's slightly slower than 5744; you can try a direct substitution and work up from there safely.

Another possibility is your forearm may be rubbing on the receiver.

You should have a dollar bill to business card thickness width between the receiver and the back end of the forearm for adequate clearance.

I also bed the forearm to ensure there is no high versus low spots where the forearm can rub from recoil.

But you said you have the same problem with the forearm removed.

So where are you resting your barrel when you benchrest shoot? Have you found the sweet spot for your barrel where you should always use to rest it at?

I get 1 MOA accuracy with 52.7 grains Swiss FFFg black powder with a .060 grain vegetable wad and a 422 grain Paul Jones Creedmoor bullet with my .40-60 Maynard CPA.

I would like to thank everyone for their thoughtful responses. 
The 5744 seems to be a touchy subject.
Thankfully, 4198 is readily available. I will work up some loads with 4198.
After I find the charge weight I may play with the bullet seating depth.
How much effect would shortening the OAL/bullet seating depth of the cartridge have? I would assume the slightly etching the bullet in the rifling is the goal, but the Hepburn does not cam closed like a HW or Sharps. The Hepburn is pretty unforgiving about this. (Highwalls will spoil you)

I shoot several Hepburns, and I seat my bullets to just touch the rifling, not so firmly they wont easily chamber. Same for my Rolling Blocks as they don't have any camming action either.

Considering all described, I would change powder. Agree with you on 4759 I use my supply sparingly. Have found 4227 to be a useful replacement. Omitting the wads would remove variables too. You could go back to wads after testing another powder.

Boats