Garter Intarsia Stitch with Diamond Jacquard Design

I would like to knit a placemat with a diamond jacquard design using garter intarsia stitch. I will have a one color frame border and there will be 7 lines of different diamond colors. I plan to use a pink color as the background color in between these 7 different lines of diamonds. Now as it is I will have a ton of numerous different colored yarns in the back that I will be working from in order to make the diamonds and would like to figure out a way to be able to use one yarn for the pink backgound color without having to have to tie that particular yarn in 7 different balls to do the stitch … which would end me up with 14 different threads of yarn hanging in the back to shuffle through as I do my rows.

Any suggestions how I could make this job easier on myself?