Einstein's 1905 Annus Mirabilis papers seem like they easiest of the bunch to just read through. I just pulled up 'Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen', the one about Brownian motion, and read the whole thing. It's only 12 pages and fairly accessible; more prose than equations.

(Of course, if you don't read German, you should get yourself a translation.)

See https://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstei...

I don't think I'm smart enough to casually read and understand original works on General relativity, but the Annus Mirabilis work seems much simpler. The famous E=MC2 paper is only three pages.

See https://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstei...

About Gödel: if you are interested in the theorems, and not necessarily their original presentation, you can get plenty of rigorous modern treatments. It's very common for mathematicians to work out simpler proofs and more appealing presentations of famous results over time.

See https://dn721807.ca.archive.org/0/items/uber-formal-unentsch... if you want to give one of Gödel's work a go. It's only 26 pages. Footnote 48a is especially interesting. Overall the prose is crisp, but the notation is rather archaic to modern eyes.

I agree with your general sentiment, and your heuristic in general.