I was thinking maybe necking up Jamison 577 Snider brass to .585 or .620 and loading to 2.65"
to fit the magazine.

The rim is right and the case would be close.

What do you guys think?

Snider brass is essentially 24 guage -- too small in the base. I would go with Magtech all-brass 20-gauge shells, or better yet, turned brass from Rocky Mountain cartridge.

I was thinking more rebarreling to the cartridge described above.

some estimates with quickload would indicate a .620 catridge would hold around 140gr of water and be able to propel a 900 woodleigh at 1500fps@30kpsi. but with the type of action why not just do a 20ga from hell or a 600 nitro. are you just looking for a catridge that will fit in the stock mag?

p.s. dont take my quickload data as gospel just a rough estimate