Problem with .410 slugs for barrels with no rifling, is the extremely light weight due to the hollow based designs.

Now, if a person had a .410 SXS with 24" tuber and full chokes, I'd like to open the right tube to mod. choke for better patterning, then rifle the left one - about 18" twist and use 210 to 240gr. bullets in it with either smokeless for black-type loads or straight black powder.

For slug loads to use in .444 cases, check low pressure, extremely light weight cast bullet loads for the .444 Marlin.

The lightest bullet weight I can find in Lyman's 1973 handbook is 205gr.
Loads around 10.5gr. Red Dot, 11.0gr. Green Dot, 12.0gr. Unique, 15.0gr. Blue Dot, 10.5gr. 700X, 13.0gr. SR7625, 14.0gr. SR54756 will produce in the 1,340fps range. These are the starting loads in the manual and should work just fine. I would use a filler (foam) between any slug and the powder. 2 or 3 round balls that fit the muzzle might actually be a decent load.
A .395" round ball in hard lead will weigh about 90gr. - so- some minor extrapolation of loadings would fit here.

215gr. cast bullets in the .444 start with about the same loads and velocities.

For a 3-ball load (245gr.bullet), the suggested starting loads are exactly .5gr. less than those listed above. The velocities run 1,200fps to 1,300fps.

If you have access to really old manuals, perhaps anything listed for the various BP .40 cal. short cases would be appropriate.

Some examples: .40/60 Maynard, .40/50 Sharps Straight, .40/60 Winchester, .40/60 Marlin, 40-63 Ballard, etc.

The second number here is the black powder load.
COTW lists 20.0gr. to 26gr. IMR4198 with bullets from 210gr. to 300 for these rounds, for nitro-for-black loads.
These are quite 'soft' loads.