Hey bud. Sweet pump!
Sounds like you have a good start to it.

Your right on some of the details on the 996. There are two different trims and how you open the door depends on what type of trim. It took me forever and a heck of a lot of messing around to get the doors open on mine as I have the same one as you but with the different method to open the doors. Unfortunately I didn't have the one with the screw in the middle of the trim that opens the lock so it was a big job since they couldn't find the keys! Mine does have the key number on the serial plate. I am expecting that there is two explanations for the slight differences between ours - either its the time period (mine has a manufacture date of 59/50 which would be earlier in the manufacturing life and perhaps you have a 51-53) or mine is a 996C which designates it as a Canadian model and perhaps the US models have minor differences.

I have the exact same pump in pieces right now in my garage. Its my first resto as well and has been a long time coming - especially since its a heritage/family thing.

if you need any help at all or want some advice, please feel free to reach out. Hopefully i can save you the same mistakes that i have learned about!
Also check out my restoration thread. I was determined to take a ton of pictures both so I know how to put it back together again and in situations like yours to help get some added insight.

That door corrosion sucks! I have similar in places. Luckily not as bad or frequent. I have gotten advice to remove it via a hand sander. Haven't tried yet as I am sending mine to sandblasting.

Side panels - those are easy.....once you start stripping. I started by removing the top (which was a battle in and of itself) and got access to screws there. There are 2 side mounted screws internally that were easy to pull once the doors are off. I'll have to dig to see if I have any additional pictures on this that I didn't post that I was saving for re-assembly. Nozzle slot sucked to get out. There is a brass pipe that is connected if I recall which has to be disconnected. the slot is basically a big drip tray for any gas that drips out. once I got the doors off and the computer removed, it was easier to pop out. The side also won't come out until thats removed. Another thing I learned the hard way! The crank handle is slightly different as I didn't have the plate around it. I had to remove the crank mechanism in full to remove that side panel. I believe there was a pin locking the crank shaft internally and it slid out easy. I would start with that side first and then work on the other. Also the hose return slot can be a problem. You'll have to remove the handle (mine was welded on I swear) or cut the hose (Another thing I did.....which bled old gas and gunk out - wear gloves and have a pail handy. Also be weary there is a metal line that is within the rubber to help for safety reasons o cutrting it means cutting through that as well). If you have the opposite side panel off first you have full access to the hose slack as well as the weight and it should be easy to remove.

Thats all I have off the top of my head but If I recall anything I'll post.