Yep. Had that done, along with the crank when my engine was built. Unfortunately, I sprayed everything down w/ carb cleaner which removed any (painted) reference marks the individual parts may have had. I then had to examine every sq. inch of the flywheel, pressure plate and diaphragm for discreet markings left from metal to metal contact and/or nuts, bolts & washers in order to reassemble everything in it's original (balanced) position.

I felt like an FBI ballistics expert matching a bullet to a gun barrel. But, I guess it worked. The A series motor was never as smooth as a Swiss watch to begin with, but as I've mentioned, mine's at least as smooth as it was before I tore the clutch assembly apart. 

Generally what will happen when you send these off for balancing is the balancer will align the A on diaphragm with the timing marks. The back plate can be in one of three position as of course it can be rotated. They will most likely check the balance in all three position and then set the backplate to the orientation with the best balance. From there the assembly will be balanced and have weight removed from various spots to dial it in.
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Update: I was successful in getting my new clutch installed. Unable to find any obvious alignment markings, it was suggested that I look for "witness marks" on the flywheel and pressure plate in an effort to reassemble everything as originally balanced. I carefully examined the flywheel and pressure plate with a jeweler's loupe. There weren't any dramatic telltale markings, but I did my best and seemed to have gotten it right. The motor is at least as smooth and vibration-free as it was before disassembly.

It took me several days to dial-in the clutch throw. The pedal is now right where I want it. There is a bit of chatter as I engage the clutch, but I'm assuming that will gradually disappear as the clutch plate beds in. Thanks everyone for you help.   

No, the slot in crank and flywheel is offset to one side, this prevents the flywheel from being fitted 180 degrees out.

Try resetting the crank to TDC by observing piston no. 1 and both valves closed or the front timing marks if they are still viable. Then check the flywheel for timing marks if they weren't erased by the lightening process. That should get yopu lined up.

It seems that the keyway aligns at 12:00 o'clock AND 6:00 o'clock, which allows the flywheel/crank to be 180° out. Yes? If that's the case, how should I proceed?

All you can do is guess backplate position.

As there are no obvious alignment marks then next best guess would be that the holes are on the horn that aligns with timing marks I guess. 

You can't get the flywheel out of position with the crank as the keyway in both is offset to prevent this.

I've identified timing marks on the flywheel and the "A" mark on the diaphragm, so I'll be sure to line them up. I've examined the pressure plate with a jeweler's loupe and the only thing I see are 2 drilled holes and an intentional grind mark all in one location that I assume were put there during balancing. Any idea how the holes and grind mark might relate to the timing marks and the "A" on the diaphragm? Also, I just realized that the crankshaft was probably balanced along with the flywheel/pressure plate/diaphragm assembly. Any idea how to relate the crankshaft with the other items? No. 1 cylinder @ TDC perhaps?

Your flywheel and backplate are aftermarket so will not have had any balance marks on them as supplied. 

Generally what will happen when you send these off for balancing is the balancer will align the A on diaphragm with the timing marks. The back plate can be in one of three position as of course it can be rotated. They will most likely check the balance in all three position and then set the backplate to the orientation with the best balance. From there the assembly will be balanced and have weight removed from various spots to dial it in.

The backplate horn that aligns with the A on diaphragm and timing marks with probably have been dot punched as the is the one to align with the other two marker points. Maybe have a good look at the back plate horns to see if there is a mark on one of them, then align that horn with timing marks and A on diaphragm.

I need help reassembling my non-verto clutch. I understand that the flywheel, pressure plate, and clutch cover have an embossed identifier (sometimes an “A”) that must be lined up with one another for balance. I marked each one with a sharpie during disassembly just in case the factory marks were illegible. When it came time to button everything up I realized I had wiped off my sharpie marks, and of course, except for the clutch cover, the factory marks were illegible. 

I had my flywheel and pressure plate lightened and balanced when my engine was assembled and there are balancing holes drilled in both. I thought if I aligned the balancing holes with one another the flywheel/pressure plate assembly would be in balance. Does this make sense? Unfortunately, when I fastened them together, the closest I could get the balancing holes to align is about 30° off, given the bolt pattern of the flywheel & pressure plate. And I don’t know how the “A” on the clutch cover relates to any of this. Any ideas would be appreciated. I’ve cross-posted this in a couple of forums, so please forgive the redundancy.