Use cap difference hello? It's a ctf tournament. Whoever made the argument of cap difference being an unfair tie breaker, good defensive teams in the world cup or other tournaments (greece winning the euros with very few goals scored as an example) still manage to do just fine with a low number of goals. It's just more incentive to push for a three cap instead of sitting on a 1-0 or 2-0 lead. Also rewards not getting capped on.
Head to head victory is first tie breaker between two teams, second tie breaker is cap difference (+/-), third breaker is flags capped. Fourth tie breaker can be sudden death to first cap (not first kill lol what) or seeding. I'd prefer first cap tbh, but the odds of this occurring are really low.
If three or more teams are tied, then cap difference is first tiebreaker, flags captured is second tiebreaker. Rank/tiebreaker is third.
Challonge even has tiebreaker options for this stuff. Literally Google round robin tiebreakers. It's not that hard.