I've owned or shot all the guns you mention. I've seen all of them many, many times in competition.
The Rossi is good for what it is -- an inexpensive gun.
If you're set on the 1892 design, try to find a Browning in .44. Many of them run very smoothly.
Do not even think about an 1894 in a pistol caliber. The '94 was designed for rifle length cartridges (.30 W.C.F., 32-40 W.C.F., and 38-55 W.C.F.) So, the gun runs poorly with pistol length cartridges. They cannot be made to run consistently. I've watched a lot of disappointed competitors over the years who thought they had something useful in the '94 only to find out the gun ruined ever match they tried to use it in.
The Marlin '94 IS made for pistol length cartridges and runs very smoothly and reliably.
The Rossi might serve you well. I ran one for a while and was glad to have it at the time. But, it quickly became more of a vexation than an asset. I was glad to get ride of it and would never consider buying another.
I've put a lot of hard time on Marlin '94s and know several guys who use them as race guns. They can be made to work incredibly well. They always require significant smithing to do so. The Remington Marlins cannot be made to work, so don't even consider those.
I think the B-92 Browning and 1894 Marlins are your only choices. Note, the 1892 action is very complicated and difficult to 'smith. The Marlin is simple and many good 'smiths can tune one to your satisfaction.
So.... In the end..... the Marlin is the only way to go. You might find a good '94 marlin with micro-groove rifling for 5 to 6 hundred bucks. I know you can find a ballard rifled one for 8 hundred bucks.