In case anyone stumbles across this in an attempt to rebuild an Edwards E2M5, I finished my rebuild and it's been humming for a week without catching on fire so maybe I did an OK job; I have no vacuum gauge so I don't know how good the vacuum is, but- it works.
I was able to figure out the position of the part 56 seal based on how badly I'd scraped up the original with the ring pliers, and it's the flatter side that faces *away* from the motor side- but that engineering manual that's on the web is just miserable. Too many parts not given the proper attention in the diagram.
The inner seal (between the first and second stages) was much more difficult. I didn't seat it straight, and lucked out when I took it to a pump repair company; when I got in there, I was feeling a little hopeless because they were working on huge agricultural pumps, with nary a vacuum pump to be seen. One of the more thoughtful engineers turned it over a couple of times, and asked "Is this out of a BOC Edwards?" There was no way to identify that pump from those parts, but he knew exactly what it was, and I told him he was bang on. Turns out he used to rebuild vacuum pumps at a previous job.
He took out the old seal, and we managed to re-use it. One little trick he used: He packed the back of the seal (where the metal spring fits) with Corning vacuum grease, using it to keep the spring from slipping out during installation- and I mean he packed it with vacuum grease, probably 1-2 cc's of grease. It got wiped clean-ish and re-installed, still cockeyed but better than I'd done it.
This has been my first attempt to rebuild a vacuum pump, and although I'd probably be more prepared to do another E2M5, I'm not sure I ever want to do another vacuum pump ever again. But if I did- this is how I did it the first time:
There were several layers of heavy polyethylene sheeting, probably 5-6 layers of 4 or 5 mil PE plastic. In the middle of all that, I put a clean cardboard box on which to put the pump so as not to tear the plastic. I also had a box of Rags-in-a-Box (Home Depot stuff), and two cans of non-chlorinated brake cleaner, and you might need three if it was *really* caked on there like this one was. I did as much as I could, and as it progressively got cleaner, I threw away the box and a layer of plastic- throwing everything into a box for disposal once the reassembly was complete, lest I disposed of a part wadded up in a paper towel. I don't think I lost any parts, but I do know I have a few extra O-rings that for the life of me I have no idea where they fit.
I'd also take pictures as I disassembled it. As it was, I used stacking plastic cups during disassembly; I find this is a convenient way to "peel an onion" like this, putting parts into a Dixie cup and then putting a clean one on top. Reversing the process usually makes it all go together so much easier. In this case, because so many of the bolts were tough to remove, and eventually (in frustration) I had to bang on it to get the first and second stages to come away, the disassembly wasn't quite so straightforward as I would have hoped. Plus, it was dirty- filthy- with heavily caked-on crud that even brake cleaner balked at. Soaking in a pail of lacquer thinner or paint thinner (I forget which) helped, coupled with a brass-bristled brush; Nylon bristles won't cut it. I would strongly recommend a box of gloves, discarded regularly, particularly if the pump had an unknown history. Too many things going into the pump oil because people don't trap their pumps properly... or at all.
A great learning experience, and I am better for it, but unless I were doing it for a living and had a workstation specifically adapted to this kind of work, I'm not sure as I'd want to do it again. The local vacuum pump place charges $1100 to rebuild an E2M5 (total rebuild), so financially it was worth it to me.