I was thinking just the opposite, raising a bit at the higher end. Since most of us cap our spread, fairly early (I max bet by TC +4), you could add an even higher bet, which I refer to as Super Max bet at a higher TC and advantage. This will increase you win rate some, not a great deal, because of the low frequencies this opportunity will occur. It really isn't proportionally adding higher risk, since the optimal spread really already allows for this. Most of us just don't do it...we cap instead.
The down side is this larger spread at the times you hit the super Max Bet count will likely draw more attention. I, myself exit after showing my regular max bet, so it goes without saying that I would exit after showing this "super Max bet". Trying to go back to a small bet after max bet is problematic enough, attempting to do so after playing a "super Max bet"....might as well tattoo card counter on yourself.