If you have a case, especially one presumably of this profile, then many firms would take it for no up front cost with an expectation of some cut of the damages.
But then Mojang sent the money without a contract. The writer thought he was working under some conditions, the company thought he was doing it under other conditions and they never actually agreed to anything. Sending the money without a contract is just as sloppy as sending the work and I really don’t see how the author would be responsible here.
Not having a contract does not mean that Mojang’s terms are in force.
It depends on those initial emails and what was agreed upon. Assuming no information was left out and he truly said "The contract was for a comprehensive buyout, signing away all my rights forever, which was exactly the thing I’d told Carl that I never did with my work", it could be presumed that what he was paid for was essentially just a license to use his work for the Java game.
Then he would have been told as much by any lawyer he approached. Point was that not having money wouldn't be a nonstarter.
And of course, even though he said he didn't approach anybody, the speculative part of my brain actually thinks he informally may have done so and received such advice (that he didn't have a case) and conveniently omitted as much from the narrative.
I doubt any lawyer would bring a suit against one of the biggest corporations on the planet on contingency. Its going to be a hell of a lot of work to win even a clear-cut case against an opponent with this much resources. See also: the cave-diver that sued Elon Musk for defamation. Or Miller UK vs Caterpillar Inc (they won, but it took 5 years)