Avoid the Math
I think another shortcut, which avoids some of the math, is to memorize some of the key RCs. For example in 6D, with Hi-Lo, if I am going to ramp my bet when TC>1, I know in advance that with 1 deck in the tray, I need a RC of about 5 or better. Once I get 2+ decks in the tray I'm in the 4 or better zone, 3 in the tray is 3 or better, etc.
During play, I don't have to do the division, I just remember my key RC "trigger points." To a certain extent, looking at the tray can be done casually, every few hands or so, as long as one can remember, generally, how far into the shoe we are.