I've heard that people have done this with twitter accounts; make a new account that's private, tweet random stuff. Once one of them comes true, say, "bart simpson becomes president in 2020", delete all your other tweets, rename the account to something like "bartsimpson2020", and then publicize the account.

You now have a timestamped thing from before it happens that verifies you made the claim long ago, but you've destroyed the evidence that it was effectively random.

"One solution would be to encode the prophecy into a blockchain, and reference that in the envelope. This way there's multiple witnesses that you did something that day at least."

That's the basic scheme. Variants on this idea have been in use for centuries. Modern hash schemes, including those used in the blockchains, make it trivial, albeit at the price of byte-for-byte precision; you just have to provide reasonable evidence that something existed at some point in time, which is easy with twitter, facebook, google, and literally thousands of other places you can stick arbitrary content that will end up with a timestamp that you can reasonably claim you have no ability to forge.

Mail it to yourself.. You'll get a postmark with a date/time it was processed. Don't open the envelope once it arrives, and now you've got proof of when you mailed it.

You need to consider what steps will be taken to eliminate fakes - at some point immense processing power, massive storage, massive memory, and AI will make a local dataset out of all the comments on all the websites and the grandparent might be automatically filtered out specifically for this conversation...