The RMH is a beautiful gun and looks more like a Hawken than anything (commercially) on the market today and one of the closest replica's ever done period (with the Hawken name tacked somewhere in the model name).
And yes, 1:24 is fast for "patched" roundball, but as has been stated give it try - keep your powder charge down a bit and see where it starts to get "whacky".
If you can't get a patched ball to work, but still want to shoot a "ball", I suggest you give Hornady "hardballs" a shot. They are a "roundball" but it's contained in an "unmentionable plastic cup".
They are designed for (primarily), non-side lock, plastic tree stocked rifles that use primers more at home in a shotgun that find themselves being used in a primitive hunt that requires a roundball to be used (instead of the more typical plastic wrapped pistol bullets).
(sorry, skirting the rules here just a little)
Of course there are some decent conicals out there (maxi's, great plains hunters) which would turn the rifle into a real "thumper".
One last thing you could try would be a ball-ete. Buffalo isn't making them any more but Hornady makes the PA Conical which is the same thing - half ball half conical coming in at 240 grains.
I shoot them in my 1:70 twist 50 cal (which gives you the thump of a 54 cal ball).
They were (engineered) for 1:66 twist, but when talking to the Hornady rep he told me that they have tested them "effectively" in 1:32 twist (which was the fast twist Lyman barrel). So something else that may work in your rifle.