Long story short, I need a shim to offset my muzzle device far enough from the shoulder of the barrel to reach 16”.

It’s a 5/8x24 thread pattern. I’m currently sitting at 7/16” out of 10/16” engagement between the device and barrel (shim is taking up 3/16”).

Ignoring issues of concentricity (I’m fairly certain it’s not going to be an issues based on the manufacturing specs of the shim), is that enough to get a proper pin and weld done?

You will be fine. As long as there enough thread to drill a divot for the pin to drop into you are good. Does not take much at all. The ATF does not have hulks waiting to use cheater bars on a wrench.