The most likely source would be for me to donate them to the genesis transaction myself. For example, I could use 1.0 BTC that I haven't otherwise encumbered. Or a collective of EAs could donate small parts of it so that no one feels they own a particular stake in it. (Maybe 10.0 BTC would make a better starting point, as there would be a billion possible sub-units (satoshi) that way.)

After that, there would still be the question of how to best distribute them. I could e.g. feed them through a mixing service and thus ensure that they are owned by random (anonymity-seeking) individuals. However it would probably make more sense to donate them somewhere that provides good evidence of utility, instead of probable drug-users.

A place like GiveWell might make sense. However I'm not sure direct donation a nonprofit institution is best for the context, as a priority would be ensuring that they go up in value over time, which would be partly contingent on them being held and prized by people. A nonprofit with an immediate use for the money might just sell it on the market for USD, which would mean that a lot of the value from early-adopter effect goes to speculators (which isn't really what I'm going for).

They could instead be distributed directly to sufficiently tech-savvy homeless people, or perhaps (as with GiveDirectly) to poor villagers in economies where money is scarce. (The client would have to run on a smartphone.) The idea is that people with almost no money would be the most motivated to try and sell them at above previous market rates and/or trade them directly for the high-utility goods and services they need (metal roofs, etc).

So I'm still thinking about the details on that end, as well as whether/how hard to try to make a profit.

It's worth noting that Bitcoin has attained its value primarily by being hard to come by within the context of a game-like setting, i.e. mining where the person with the most effective hardware wins. I could end up doing that with some or all of the coins. If I were to use a proof-of-work distribution system, I would probably use something less parallelizable such as scrypt hashes. (Litecoin uses this, but is otherwise an alternative blockchain of bitcoin -- it is not a colored bitcoin like this would be.)

There are ways to make alternative schemes for proof-of-work function within the existing bitcoin protocol, for example attach some coins to a private key that is the result of a greatly expanded version of a smaller seed, and publish only part of the seed. The missing bits would have to be guessed repeatedly, and the expansion from the original seed would have to take place each time, before someone could claim the coins. Difficulty would be determined by the number of missing bits.