I'm making some assumptions here: those look like M5 roofing type screws. As Ampex was (is?) a US firm did they use UNF fixings? I assume the screws go through the wooden side panels and into a threaded hole or captive nut in the metal chassis. It could be a trick of the light, but it looks as though the tip of the screw has been scraped by being put into a hole that isn't the right thread for it.
I'd be tempted by pmmunro's idea of screw cups and raised countersunk screws (probably stainless Phillips...) as they'd be a bit more classy than plastic washers, unless you want the '70s look! If the original screws are indeed an Imperial thread form, then screw cups are available for various gauges.
For example, at Bresco. Notice some are countersunk so the washer itself sits within a countersunk hole to spread the load of the screw head, while others have a turned flange that will bite into the wood.
An alternative is the turned cup washer which has a flat back so will not bite into the wood, but also sits above its surface to support the screw.
Spalding have a selection of these.
If you want to reproduce the original, I think a search for 'plastic shoulder washer' will get you close. Good luck!
Edit: Ha! Looks like we had the same idea at the same time...