If the service disconnect is no longer in this panel, then indeed the grounds and neutral need to be separated. You need to have a GROUND WIRE and a NEUTRAL run from the service disconnect to this panel, and separate ground and an (isolated from ground) neutral bus. The branch circuit grounds and neutrals need to land on the appropriate bus.

On a HOM panel, you need to purchase and install a ground bar (or bars) that mount directly to the case. The incoming ground connects to one of these as well. You remove the bonding screw (it's on that crossover bar connecting the two existing bars, probably behind the wire feeding the main breaker on the left side) to unbond it from the case.

Yep that is what I was thinking. I will have to find a bus bar for the ground, and see if there are mounting holes to attach it to the box somewhere.

Most of the label on the interior of the box is warn off, but it looks like the bonding screw should be in the hole in the center (between the two hot wires), but it is not there. So I want the case grounded, not bonded to neutral, so it should be correct once the ground bar is installed and the grounds and neutrals are placed accordingly? I can ohm between the neutral bars and the case to double check.

As far as pulling a new ground wire from the main outside into this box, it looks like #8 copper? ( If BONDING JUMPER SIZING (Table 250.102(C)(1)) is the correct section?) I've got some green coated #6 thhn that should do. The entrace cable is #2 aluminum.

It looks like that's an older HOM panel and I'm pretty sure it will be on the crossover bar, see where the tip of my arrow is (look behind the big black conductor feeding the main).

Your panel looks like it's fed with #2 Copper. I don't see why you think it's aluminum. # 8 copper would be an appropriate grounding conductor then.

I don't know why I said aluminum. It is definitely copper.

There is a hole behind the left feed wire and the one in the center of the crossover bar just right of your red arrow. Neither have a bonding screw installed. Should be good there.

So the new #8 ground will be put on the new ground bar installed inside this panel and will be connected to the buss bar in the main disconnect panel, correct

Yes, you need one of the Square D grounding bar kits. You'll need one that has at least one larger terminal. The following qualify: PK15GTAL, PK15GTA6, PK18GTAL, PK23GTAL, or PK27GTA. The others only have holes for smaller (14 or 12) wires.

Perfect. Thanks for all the info. Much appreciated.