.44's
When the Ruger 77/44 came out, I was very so-so about them. I really liked the semi and lever .44's and if given a choice, would go with one of that variety. But the levers and semi's are gone, and prices are soaring. The bolt rifles are still with us, I think, and reasonably affordable. So you gotta use the tools you can find (or afford).
Ruger got the twist rate right on the new .44's and I would try and take advantage of that and drift towards the heavy end of the scale. I don't know if the 265 gr JSP slug is offered as commercial loaded ammo or not, but I would look or load that as a starter. I would not drop below 240 gr ever in the new fast twist carbines, esp for hogs. Many of the 180-200 gr slugs are intended to expand at handgun velocities, and from the speeds possible from a carbine tube are somewhat fragile. A big hog shoulder or raking shot may offer a substantial obstacle to a light .44 JHP intended to expand at 1000 fps.
As far as optics go, I don't really see the need for more than 4x on your rifle. The .44 has near mortar like trajectory, even from a carbine, and more X power is not needed for the effective range of the .44. Too, .44 carbines are pretty tidy rigs, and why burden one with more glass than it needs? I'd avoid a "full size" scope for that reason. I'm thinking a compact fixed 4x, maybe something like the Burris Timberline (?). Never used one, but the X level and size seems about right. If you like variables, a Leu 1-4x or something similar might be the ticket.
A stainless/synthetic 77/44 should be one rough and tumble carbine, and that may offset my original attitude on the bolt .44's. The old levers and semis were not available in stainless but the 77/44 is, or at least, was. Hmmm!