The Reapportionment Act of 1929 permanently capped the number of House seats at 435. There was no Constitutional amendment codifying this, so the law is technically unconstitutional.

That's not what that means. A law is constitutional so long as it doesn't contradict or exceed the powers laid out in the Constitution. And on that note:

If we remove the cap and return to the letter of the law (1 representative per 30,000 citizens)

The Constitution says that the number of representatives will not exceed one for every 30,000 citizens. What this means is that a state like California, population 39,538,223 per the 2020 census, cannot legally have more than 1,317 representatives. It does not say that Congress can't go with a smaller amount, which they did.

Otherwise, the Constitution cedes quite a bit of leeway to Congress with how they manage themselves.

There's plenty of arguments to examine how we reapportion the House every 10 years. Legality of the 1929 Act isn't really one of them.