I see that the 444 was not a factory chambered barrel, it was a 44 mag bored to a 444. Were the mount holes drilled too deep? Were extra mount holes added? It is hard telling what was done to that barrel. I know that SKS bases several of their priority cartridges on the 444 Marlin for the Contender. They have done hundreds with out problems that I am aware of. I know that some Gunsmiths like to add extra mount holes and opens them up to #8 from a #6. Was that done to this barrel? Who knows.
I said that as a rule of thumb based on the fact that when you make a stub, you make the liner chamber walls at least as thick as the Contender, so anything in the Contender, should be safe in a Stub. I agree with Tim that you need to be cautious when you start getting into unknown territory, you need to be very cautious and know that for every thing that is done, there is a trade off. If you make the chamber walls thinner than a Contender, then you need to chamber for a smaller case.
The larger in diameter the case, the more it needs to be down loaded. You can buy a 45-70 barrel for a Contender, but you can only shoot trap door loading (level 1) in it, safely. You would just be asking for trouble to shoot level 2 or level 3 in it and so the same for a stubbed Handi. A regular Handi will handle level 2 loads with out a problem, but not a stubbed barrel. I only have 1 stubbed and it is a 22K Hornet...plenty of chamber wall for it.
Good Luck and Good Shooting