Are you sure this was a 6-deck game? I’ve heard of this bet on an 8-deck game with a 3.37% house edge, but those payouts on a 6-deck game shoot the house edge up to 5.79%. That is truly a greedy casino!
Unfortunately, I don’t think this bet can be sufficiently beaten using traditional card counting. The problem is that the red+black bet and the red+red/black+black bet are always fighting against each other. You want an abundance of both colors to get an edge at the red/black bet, but that makes the other bet less likely to occur. Similarly, when the remaining cards are mostly one color you are less likely to win the red/black bet. As soon as one bet starts to turn positive the other one turns negative. The result is that the house edge tends to hover around 6% despite the “ethnicity” of the shoe.
One way to beat this bet would be by tracking the relative number of each rank and waiting for a significantly uneven distribution. That would be very difficult and may not occur very often (as you noted). This bet could also be beaten by using some sort of sequencing or tracking, but that is far beyond the scope of this public forum.
-Sonny-