You need a tournament structure that rewards wins more than punishes losses.
Graduated cut from FFG's own fundamental tournament document fixes many of these problems by rewarding the top players with byes in elimination instead of draws in swiss and is actually recommended for large events.
If you want to TO a tournament, but don't want to break the rules, you can run your tournament with this structure and ID won't be an issue.
Unfortunately, assuming players know the number of rounds at the start (which they should be informed of), the top tables can still ID knowing they will be part of the cut. In the Graduate 24 + 8 example if it works out to a situation like Roanoke, where after the next to last round the 24 players are set, they can just ID gain one more point than the next 8 players can possibly achieve, locking those players out of the graduated cut.
Another problem, besides the extra time requirements, is that this graduated cut is "usually followed by additional Swiss rounds", meaning after the first graduated cut, some players will be in a position to ID into the final cut. It unfortunately won't make IDs a non-issue.
