I think the Ruger 77/357 pairs up with a double action revolver better than a lever action, and it is not semi-auto about which you are concerned. Where you get into trouble is actually intending to cut costs and shoot 38 Special. Then the rifle of either type doesn't function or is not at its best. However, I too have seen a new Remlin work perfectly shooting 38 Special. It was cowboy action with 10 rounds, but the newer shooter was not at all fast or testing the action's ability at competitive speed. The gun had no work done to it.
The 77/357 has a five round rotary mag,, while the lever actions typically hold 9 or 10. The 77/357 is less likely to encounter a law about round capacity, if you can imagine an 1866-1892 design being condemned. If five rounds seems like too few, consider that additional mags can be carried and I expect to remain legal.
The Redhawk doesn't measure much differently than a Smith N-frame and can share some of the same holsters. Neither gun was intended for concealment, especially the Smith as a police gun carried openly. What I question about the interest is round count. If it holds more than six, you know it is in a platform intended for a larger caliber. I had a 5" GP100 full lug that had no problem shooting the full range of 357 Magnum. The GP100 Match Champion I have now is more of a handful but is up to the task and a more practical gun. Same thing for the 4" S&W 686 I had. You could simply opt for a full lug GP100 with a longer barrel, 5 or 6 inches. Grip choices help with any recoil issues.
The advantage of a loading gate is to be able to quickly, although not fully, reload, even one-handed in the right circumstances. That is why tube-loading Henry Repeating Arms rifles are allowed but not favored in Cowboy Action Shooting.
If you favor a lever action rifle, then the more logical pairing of a revolver would be a single action Blackhawk or Vaquero, noting that you, like me, might prefer to shoot a Redhawk single action in any case. The Redhawk trigger in either single or double action is not the stuff of dreams. The catch with the Blackhawk or Vaquero is that you will probably not get a full grasp of the grip. I would pass, if you are immediately going to go with a poorly fitting Pachmayr rubber grip. Those guns have enough mass to handle the recoil, so it's really a matter of gaining some skill with that type of grip and learning to let the gun roll rather than fight it.
I guess I have spent my two cents