if you already have the parkerizing solution, you can touch it up with it as well,
just heat up the solution and using a qtip or similar, dab it on the spot,
sometimes cold blue will leave the spot 'bright' vs parked,
takes a bit to card that down and redo, card down etc to get it to look right
Anything used to fill pits won't take the phosphate finish. Would look better just finished over rather than trying to fill them.
this, unless you are a really good TIG welder,,,
if they are not too bad you may be able to use a more coarse sandblast media, but be careful with that,
a friend redid a poorly treated Colt 1903 using a good draw file,
he worked it carefully, you can hardly tell it was abused in a previous life once it was reblued,
J. B. Weld was mentioned as a filler for the pits. You can fill the pitted area by welding over, but it will have to be dressed down, and then sandblasted to match the resto of the pistol, and then will probably come out a different color under the phosphate. The ends of the slide were hardened, and were normally darker than the rest of the pistol.
Try painting on the rusty surface with a light coat od turpentine and rub with bronze wool or brass brush. might have to lightlypolish with a FINE wire wheel/
If the gun were mine I would take the exposed parts to a machine shop and have them lightly bead blasted (if you don't have access to a bead blaster) then re-park in the light gray finish.
If the pitting is light (which it doesn't sound that way) you could perhaps use your tumbler to clean the parts then re-park.
Being a shootable Remington Rand it will always have some value but mostly it will be a shooter from here on out regardless.