If you only need to remove the core it just lays in place and can be removed by separating the two halves of the box. Unfortunately if the core has never been removed before the entire box will need to be removed from the car to access some small sheetmetal screws on the back side next to the firewall. You might check to see if those screws are still in place because often if a core was replaced or worked on previously they were left out so the entire box did not have to come off again.

If you need to remove the entire heater box the procedure in the manual linked above explains where the nuts holding it are located in the metal air diverter box inside the passenger compartment. A couple of the nuts are kind of recessed and somewhat hard to access. If they are rusty it may require a bit of work to get them off. There may also be additional sheet metal screws on the engine compartment side added by dealers so if the nuts alone do not seem to release the box look for hidden screws under the box or around the round vent opening that go into the sheetmetal. Once the nuts and any screws, the fabric duct and the flapper valve cable are removed the entire box and vent tube assy will lift out. Removing the small sheetmetal screws that fasten the two halves of the box together will provide access to the core. A gasket material which could have deteriorated and became sticky may want to hold the core in place but there should not be any other fasteners.

Does this help? Page 3
https://packardinfo.com/xoops/html/downloads/servicemanual5154/Accessories_III.pdf

Can someone provide a procedure or link for a description of how to remove this?

If you are handy, you might consider repairing the ammeter yourself. An ammeter is just a small coil that creates a magnetic field and moves the needle. They are very simple.

I couldn't stand that green fender on the car anymore. So I pulled it off, straightening and welded some minor tears along the bottom flange. I removed all the scale rust and mud from the inside of the fender and then shot the entire thing in red oxide primer just to give it something. Then I painted the fender in rustoleums finest black rattle can paint making sure to do the worse possible job I could. When I get back from NZ I'll scuff it and scrape it just right to let the red oxide show through in places to compliment the rest of the car.

These were the best of the styling-smooth!!!

I was referring to the cover on the smaller shaft which still appears to be incorrect, wrong shape, inside diameter too big for the shaft and has a non-Packard part number on it.

Correct, the larger is for the 356 only but I see six holes in the cover so maybe the angle of the photo hid a couple.

The one with the larger shaft diameter is for the Custom 8 356 engine which has a different clutch disc and pilot bearing.
The smaller one is for the 288 and 327 engines but the cover plate that is with it appears to be incorrect with only 4 mounting bolts instead of 6.

Yes rear wheels off the ground would help determine whether the transmission is free. Service and parking brakes should be off. If you have a helper to depress the clutch, you might try rolling the wheels. Depending on progress/results you may consider removing the drive shaft. Have you read the caution about OD stuck engaged and trying to back-up?