I think the tile-picking might be simpler than you're imagining. I strongly suspect that the best picking strategy is essentially going to be to start with __ZQXJK, and then just split the rest. There are even numbers of everything else except A, I and G, in fairly useful proportions. Probably nobody really wants that many Us or Os, but by the end that'll be all that's left...

I've heard it said that there are more possible games of chess than there are atoms in the universe. Chess is, in some sense, unfathomably complex. But, there are a number of rules or heuristics that one can use to play a better game of chess. Your queen is more valuable late in the game than earlier in the game. Aim to control the center of the board. And so on. For those of us who aren't Kasparov, we can still play an enjoyable game by following these heuristics. That is, it gives us concrete goals that increase our chance in winning.  

This variation of Scrabble, I would guess, has even more possibilities than chess. I'm no Scrabble expert, but I'm having a hard time imagining what the similar heuristics would be for this variation. That is, what would be the good strategies for picking tiles?  

I think if I played this game today, the tiles I pick may not be substantively different than a random sorting. As a non-expert on regular Scrabble, the words I play are basically maximizing my points given the current board and my tiles. Except for maybe ruining a prime space on the board if I can't utilize it myself, I don't really play strategically, anticipating what my opponents will do. But this still gives me a concrete goal that improves my chances of winning, and a small enough number of possibilities so that I feel I may have actually succeeded in maximizing points that turn.  

Imagining playing this variation, I feel mentally paralyzed. The simple heuristic of maximizing points given the board and your tiles seems woefully inadequate when the number of tiles in your tray is significantly larger. And while ignoring the tiles your opponent has in standard Scrabble isn't the worst thing in the world (since you only have imperfect information anyway), it seems inescapable under this full information variation that you have to consider your opponents' tiles as well as your own.  

Or in short, my wife has trouble making decisions. Would we ever finish a game of this Scrabble variation?  

I am intrigued by the setup; I'm just wondering if will actually be playable.  

One thing I do foresee is that the endgame will be far more important. In regular Scrabble, the points deducted at the end of the game are limited by what you have in your tray. In this variation, since all players start with the same number of tiles, your exposure at the end is raised significantly. So I'm thinking one heuristic would be to place even more emphasis on getting rid of your tiles as soon as possible.

I thought about leaving all the tiles in one big pool, which is what your friend's variation more or less amounts to, but I think that would mean that everybody plays MUZJIKS on the first move, and whatever the best next play is on the second, and so forth for at least the first few moves, which would clearly be boring. The tile-picking round prevents that, while incurring (I think) a much smaller number of "necessary" moves.  

Actually, thinking about this gives me the idea for one further rule-tweak to make the beginning more interesting. In the spirit of having to move pawns first in chess, the first word by each player must use only 1-point tiles.

An old friend of mine taught me a game he called Guerilla Scrabble, which is basically what you describe with one additional rule: you are allowed to grab tiles from other people as soon as you have thought of the word you want to play.