issues
Need to clarify a couple of issues. JHP is a pretty broad field. There are .44 Mag JHP rounds intended for SD in handguns, designed to expand at handgun velocities, typically 180-200 grains, that would not be anywhere near what one would ideally want in a carbine for black bears. Same for "solids" ( I expect you meant a projectile that was not a HP, like SP or SWC). There are also some light SP rounds that are not ideal for bear either.
Were I to brace a black bear with a .44 carbine, I would minimally want a bullet weight of 240 gr and up. The 265 and 300 weights would be attractive. The boutique loads would be optimal, as would a soft point or SWC, but I would not feel totally undergunned with a good full power 240 or up JHP. I suspect quite a few blackies and big hogs too have met their end receiving a .44 mag 240 JHP.
One note re your SWC. There is some .44 mag SWC out there that is not full power, and again, would not be ideal for thumping a blackie.
Finally, though I have been guilty of doing some very bold (stupid) things around black bears, they are a formidable wild animal, that thinks for itself. If there were a 400 lb blackie frequenting my place, I would keep a firearm handy as you describe. The animal may well be accustomed to human contact and much braver than normal. My experience 90% of the time with truly wild black bears is that they leave the area PDQ upon detecting humans. But dumbed down blackies are another matter.
A game cam pic would be cool.