I recall reading recently (in the past few weeks) that part of the problem is the model assumes time is passing at more or less the same rate throughout the universe, assuming homogeneity at a large enough scale. This assumption ignores the vast voids of nothingness where GR predicts time will pass at a faster rate, which affects how we see the time elapsed for photons travelling through those voids. I thought there was research underway to see if that would explain the tension.