The "spacer" is a mack washer turned upside down. Its nothing special about the "spacer" itself. Whats different is the exposed overflow and the mack gasket...what HJ is calling the spacer between the lavatory and the overflow assembly. Thats not typical. Usually the overflow is integral to the bowl and no extra mack gasket is needed in that space. It would be factory made into one assembly.
I'm not saying go wild and tear it all out. By all means if it stays in tact and in in good shape you cna leave that "spacer" alone.
Loosen the large nut until it stops at the bottom of the threads. if it will not turn the use a saw and carefully saw it on two sides and pry it off. It will fall into two pieces.
Now cut the lower mack gasket into with a razor knife and carefully remove it. The entire drain will now lift up and there will be a gap between the lavatory and the chromed brass flange that you see when looking down into the lavatory.
While holding the bottom "half" of the pop up assembly...grab the rim of the flange inside the lavatory with some channelocks and turn the flange counter-clockwise to unscrew it. It will come apart and the rest of the pop up assembly will drop out of the bottom. The p-trap should also be removed by now.
If the upper mack gasket is rotten you can get another at any good plumbing repair specialty store or a good hardware store thats local owned.
I like Delta or wolverine brass all chromed brass pop up assemblies. There is also an American standard brass pop up I like. Kohler makes a fine one. Dont buy a plastic one and do not buy a cheap knock off thats chromed brass made in china......they are garbage and the stoppers do not have enough travel. Grohe also makes a nice pop up.
Or you could leave the pop up alone other than getting a pop up stopper for it (readily available) and a new horizontal ball rod (readily available). Not much to be gained by replacing it if its not leaking. You being a DIY I'm not sure what your skill level is or how much time your willing to spend.....no offense intended.
Is anyone aware of a similar looking faucet with a smaller (or more forward set) footprint? Or any 40s style with an undercut in the back? I'd even be happy with no stopper pull as we never use the stopper anyway. Any ideas would be most appreciated!
we would need a picture of the sink, because your difficulty is NOT normal for any sink of this type.
That particular faucet is a PricePfister wide spread, but you said it had "clear crystal handles". If this is the faucet you were referring to in the original posting, the valves a NOT 'shot' and are easy to repair to"like new" condition.
The faucet "hole" should be the same distance as the other two, because that is the way they made sinks back then. At that time the faucets did NOT have "hoses" so all three openings HAD to be exactly in a line. But even if it is offset because of the drain overflow, your "problem" is that the spout has "overhang" at the rear. Not many new faucets use that design so you have the choice of many new ones, including all current Pfister faucets.