Grudge match
Since we created this grudge match system and we force it to execute whether we have played this team or not... perhaps we consider a "rematch" system? In rocket league my friends and I loved this feature.. you lose and feel you got robbed/ they got lucky goals, you played bad/ shots were off, so you hit rematch.. they feel they were the better team so they are happy to accept to get a second win and not have to search for a new team. Then we get the grudge match system to execute. This would also help alleviate teams getting into games with teams far better/ worse.. a team far worse wouldn't accept.. so you're effectively getting more games against your own skill level. I remember a few years ago we played the same team probably 6 times over the course of a few days and they became our rival. This system could create rivalries.