I think that tennis solved the problem by not using an ELO based score but giving points by the number of turns a player wins in a tournament. The most important tournaments give more points. All points are lost after one year. Of course tennis and chess differ in a fundamental way: there is no draw in tennis and tournaments are basically never round robins. The ATP finals have a couple of round robins before the semi finals. They give points for the wins.

So maybe in chess they could give points for each win, less than half of those points for a draw, zero for a loss.

Tradition is very important so they should keep the ELO and keep updating it according to who wins against whom, but qualifications to tournaments and seeding (if that's a thing in chess) would be based on the other score. There could be wild cards to let some strong or popular players play even if they don't have a good score. Tennis pro associations have provisions in place for players that are forced to miss tournaments because of injuries, etc.