How can I get a company's annual report from the early-1990's if they
don't exist any longer?  (the sec website only goes to mid-1990's at
the earliest)

Post a question to the SEC. Or call.

Here in the UK, I know that Companies House have archived copies on
microfilm going back to the 1920's in some cases.

However, these are not on their website so whenever I want copies of
old accounts, I give them a call.

They are always very helpful and the costs are reasonable.

Of course, you then need a microfilm reader but Public Libraries can
usually oblige.

A UK service is absolutely no use to you, I know, but it shows how
things are done in the Mother Country.

Good luck!