If your woman is constantly accusing you of thinking about other women... then I highly recommend you think about other women and get the hell out of dodge
Naw, we should have used 420 to ensure we can also cleanly divide by 7.
Maybe even 1260 so we can fit a division by 9 in there (420 already has 3 as a prime factor, so only need to go 420 x 3 to get a clean division by 9). I suggest ending there since we could divide by everything up to our number of fingers.
Using your modified Babylonian system, I think you can actually make it to 168.
Using one hand for lower digit and other for higher digit, you can effectively count in base 13 on the higher digit hand to 158 (13 x 12). But you can then count an additional 12 on the lower digit hand leaving you with 158 + 12 => 168.