As the comments pointed out, there are a few flaws in this setting. Nevertheless we might attempt to provide a reasonable path.
- Evolution is not so fast. The plan to select individuals to with particular family history to reproduce, and gradually increase the lifetime expectancy of the new born is slightly unclear ground. But I'm not a biologist. Even if we assume that it works, I'm pretty sure that a life expectancy increase of 5 years per generation is more than optimist. As in the linked post, a generation would consist of 30-35 years. On that basis, to go from a life expectancy of 100 years to 500 years, that would be 80 generations, so with 35 years in average (probably earlier for the first ones and later for the later ones) you need 2800 years of careful selection. And this is very optimistic.
- You need a rather large group. Life expectancy depends on a lot of factors, but even people with the rights genes for longer life aren't free of other risks. In particular a genetic diversity prevents you from getting everyone wiped out with the first virus. It would be a pity to go on for 1000 years, spending a lot of careful attention and secretive actions to get your 5 families wiped out by the latest flu streak, because they were genetically unprotected. And you need to consider the other risks of a very limited pool (I won't come back to that, some others did it much better than I would on other posts around).
- Hard to keep secret. A few thousands individuals living a few hundreds years, with on the whole several hundreds of thousands of people involved. Good luck keeping it secret. You can hardly get 50 people involved in something without having one of the babbling about it. The amount involved is just beyond what is plausible. The one way to do it would be to separate the whole subjects from the rest of the society. But again, careful to the evolution strike when you get out of your protective hide-out.
- This point is linked to the previous two. Old Age isn't the only cause of death. Just living longer does not exempt you from dying in another form. Accidents, injuries, illnesses, etc. you name it. Even if you get them isolated, they might fight against each other. And you might end-up in exactly the same problem as generation ship. Worse still, even their families are programmed. And it's lasting much longer!
You essentially have similar problems than generation-ships, but for longer time. And considering that the long isolation, you might have people that could make the trip, but I'm not sure they would be considered humans anymore. I think you'd be on much better ground investing on cryo deep-sleeps and AI to fly the ships.
How to get on-board
Now for the following, will hand-waved away the previous objections. Let us assume that somehow, you manage to get a few hundreds of people living up to 500 years.
You want them to be kept secret and living in the middle of the population. Due to their extraordinary longevity, you need them to move on regular basis, to avoid raising suspicion. This implies some logistics, and money, but you mentioned money wasn't an issue. However, the organisation has to be closed to the political powers on their countries. You don't get to change the identities of a few thousands people without attracting some interests by the government. And the best way to keep it silent, is to make sure that the people who's job it is to check that are looking away.
Another reason to keep close to power is that while you concentrate on building a crew for the ships, you need to be involved in any space exploration program, to be ready at the right time, prepare your crews for the specifics, and at the same time orient those projects in the right way.
These points indicates that you need some hidden, strong and continuous lobbying in the political, economical and scientific leading circles. It is preferable not to bring your new humans on the post. Those groups are usually too exposed to the public opinion to actually hide. You need to form some illuminaty-like group which coordinate the lobbying and implications. And you need to carefully avoid being identified as a united group. If you want to be in the USA, you'd probably do well to have some politicians on both side. And many people involved in your cause without knowing about it.
When the time comes, many leaders are working for you, and most probably you were the one creating the final project anyway.