I replaced the faucet in a 1930's pedestal sink, but ran into problems trying to replace the popup. It seems the sink's openings are larger than standard sizes. The original popup is 1.75" in diameter and the drain opening recess is 2.75". I haven't been able to find anything (even vintage) to match those dimensions. The original popup rod is too thick to fit into the opening where the new popup rod would go and the new popup rod is too small in diameter to fit the old connector piece. An additional challenge - the old popup is rotated up and down by turning the hex-shaped rod clockwise and counter clockwise (no pivoting).

Any suggestions, other than just using a rubber stopper?

Also, the faucet escutcheons are almost exactly the same size as the openings in the lavatory. Is there something like a chrome washer that I can put under them to be able to better tighten them to the lavatory?
Pictures are attached.

Attaching pictures.

Yes, indeed, this is a vintage drain with pop-up assembly.

First, let me give you some background information about your faucet: The faucet is not the original faucet to match the drain and pop-up assembly. The original faucet had Hot faucet with Spout on the left and Cold faucet with Spout on the right side of the sink. The middle hole was used for Pop-Up Knob. This know was connected to the horizontal pop-up lift rod under the sink. The way it operated was as follows: you closed stopper using Pop-Up. You filled Hot and Cold water using individual h/c valves. Once sink filled up, you washed yourself and when finished, you pulled on the pop -up knob to lift flopper and to release used water.

Later on, somebody replaced the H/C faucets with newer, more modern unit which had h/c handles but now it had One spout in the middle. It looks like it is Price Pfister brand. They simply removed and tossed the Pop-up knob to free the middle hole. Then, they either didn't use the pop up at all or if they wanted to use it, they simply reached under the sink to lift it by hand.

You hand purchase just about any 8" wide spread faucet to replace the one in posted photo. The faucet comes with drain and pop-up assembly. Install it. You will have to replace the trap and that short piece of horizontal drain pipe as well.

As far as the size of the drain on the inside of the sink goes - drain holes are standard size. You should not have problem with the drain size at all.

Let us know how you did... Milo