If I get my Redolfi .444 Marlin double regulated with one particular bullet, say a 325gn hard cast, how likely is it that 300gn pistol bullets, or a 405gn hard cast will shoot well?

All you can do is try it, I've had some doubles that just like one bullet and one bullet weight, I've had some that I could regulate about anything I put in them. Experiment, experiment, and let us know how this rifle shoots. I will say that cast bullets seem to be easier to regulate than jacketed bullets, but again it's quess work.

Express, in my 8X60RS, I find that all bullet weights from 150 grains up to 200 grains will be within a usable pattern with close to full-charge handloads. I wonder if it is because the rifle is a relatively small bore size and shoots bullets much lighter than the larger bore guns.....there is not as much recoil impulse t push the barrels away from their center of gravity, and at the higher velocities, the barrel time is pretty much the same for the various bullet weights??

If possible try loading some of your own. before spending money on reworking the barrels. The 444 is easy to set up for. A lee die set,and a scale is all you need to get started. Get a copy of Wright's (Shooting the British Double).

JD

Today I tested some 300gn Sierra jacketed soft points that I jimmy rigged with .44magnum dies as I'm waiting on the .444 Marlin dies.

The surprising thing was that they shot closer together than the Remington Factory 240's the gun is supposed to be regulated for.

At 50 meters rested off my patio table the 300 grain bullets were about 1.5" apart while the Remington 240's were a terrible 4.5" apart, each barrel shooting into less than one inch.

The 300's shot 3" low with the lower, wide express sight, and about 5.5" high with the finer sencond sight. This might work out to be ok if I try the loads closer and further away.
Another funny thing was that the 300's remained the same distance apart with all three powder does - 48gn H4895, 50gn H4895 & 52gn H4895, just going up in height by about 1.5" with each step.

Obviously some tuning is needed, but I feel confident I can get it right with a few more tests.