Just run the most sophisticated chess engines available 960 times and publish the results.
Even if not the "best" in an absolute sense, the moves those engines find are going to better than the move that an human comes up on the spot.
This means that memorization will still be necessary in Chess960 to be competitive at the highest levels and in fact it's probably going to be worse because memorizing those 960 starting moves sounds far more tedious than memorizing classic opening theory.
Scrabble players can memorize 10K+ word dictionaries in languages they don't know, and since (starting position, move number, chess move) triples can be encoded as words, it should be possible to memorize the main variation found by chess engines for each Chess960 position.
But this hinges on there being a computable best opening, which there isn't for standard chess and there won't be for most(all?) starting positions in 960 (chess isn't a solved game). It's also not just an enum of [starting position, move number, chess move], there's also "why is this move strong in this position" which isn't something scrabble players have an equivalent of with just memorising lists of words.
I personally can't imagine any of the current top chess players memorising hundreds of opening lines for all 960 starting positions and then being able to remember them over the board. Only a few players have a mastery of current known chess theory that's just one starting position. I am happy to be proven wrong though when some new chess savant presents themselves.
All you need is a method to compute the first white move that produces a significantly better win rate than thinking about it during the match, and then memorizing them becomes advantageous, if doing so is feasible.
It doesn't have to be chess engines (although that seems the best approach), it can also be 100 people each spending 10 days analyzing one position per day, or it can be win-rate stats from high-level tournaments once Chess960 is widely played and there is enough data.
I’m not sure you understand opening theory. It takes years to learn a single opening, and I don’t think any serious player would claim they know all variations/sidelines of a given opening.
There’s no single “best” opening because you can always employ a defence for a specific opening. For example, there’s a trap against the London which is to play 1. d4 d5 2. Bf4 h5. 3. e3...
The issue is that people are memorizing lines like 20 moves deep and memorizing strategies which exploit deviations from the known good lines. Even if people committed the same level of memorization in 960, original games would start after move 2 or 3 not move 23.
This is true, but the issue I was concerned about is that memorizing datasets is not fun, so games should be designed so that dataset memorization provides no advantage, so that competitive players aren't forced to waste their life memorizing datasets.
Solving this issue also naturally solves the game variety issue.
As for variety, there is still the risk that chess engines might be able to produce a single long consensus main variation for each 960 position, and so that even if people can only memorize one variation, everyone could memorize and play the same line.
Even if not the "best" in an absolute sense, the moves those engines find are going to better than the move that an human comes up on the spot.
This means that memorization will still be necessary in Chess960 to be competitive at the highest levels and in fact it's probably going to be worse because memorizing those 960 starting moves sounds far more tedious than memorizing classic opening theory.
Scrabble players can memorize 10K+ word dictionaries in languages they don't know, and since (starting position, move number, chess move) triples can be encoded as words, it should be possible to memorize the main variation found by chess engines for each Chess960 position.