A couple of rebuild tips for you.
That reg does not appear to have been touched since being built. If you look at the second stage you will see the standoffs have been slightly bent above the lever. Carefully straighten them before removal and once off you can straighten them more. Be careful doing this as replacements are difficult to come by. DO NOT re-bend them later, this was done at the factory but is unnecessary. Once you have them off, file off any burrs caused by the bending. The brass nut on the LP seat has been staked to the seat holder, many times the nut will not come off and if you try you will end up breaking the stem if you try to remove it directly. It is best to first remove the assembly by working a screwdriver under the lever and remove the 2 screws that hold the lever supports, remove the lever and supports. With the lever off, you can remove the LP seat assembly. I would suggest you replace the entire thing with a HPR since no 2 stage reproduction main diaphragms are currently available. You really should replace the main diaphragm if you intend to dive the reg and the HPR is much easier to set up. If you choose to reuse it, start by trying to turning the nut IN, gently rocking it back and forth to work out the stakes. If you can get it to work loose and off, great, if not, then turn it in as far as you can, it will usually go in but not off. With a 5-40 (this thread is NOT 4-40) die clean up the threads. Remember, the stem Is brass and easily broken. The good news is new LP stems are available now, back in the day if you broke it, the reg was toast.