Not in 100% agreement in all points, but if I could lock this in rather than let Turbine continue down the path they're heading I would do so with enthusiasm.
I love completionist being a free feat - it's not overpowered and being free seems a reasonable reward.
I like the idea of triple completionist being able to start at 20 and don't agree with those who think they should get such a benefit once they've simply gotten the past lives that interest them. You have to get all past lives to get the completionist feat, even the ones that are "irrelevant" to you. Similarly you should get them all to have the benefit of triple completionist. As has been pointed out, if you don't want those past lives and only want to hurry back for another epic TR you can go iconic and start at 15. That's more than enough of a short cut for those who aren't triple completionists.
An additional point: even if you have veteran and vet7 unlocked, you can't heroic TR to lvl 4 or 7. TR means starting over. You have to live a full life in order to get that past life feat. And only if there are no more past life feats left to gain should you be able to skip ahead.
There would need to be some kind of limit on fate points, what that limit is I don't know. It's true more are possible whenever they add a new ED, but that doesn't happen often (once so far). Thought would have to be given to make sure that epic TRing wouldn't result in so many fate points that it feels unbalanced.
But I really like the proposal overall. It didn't quite win me over when I first listened to the podcast, but reading it here has helped.