Yes Sandy, some of the food dyes will mordant to the paper support. Sorry. The only other way to do this is use a pigment. You might consider the pigment used for colored carbon. Just use a tiny amount to make the coating visible though.
OTOH, can you coat on YUPO? I doubt if the dyes would mordant to that support.
I could probably coat on Yupo, but for printing I prefer all rag papers.
Guess this is one of those times when the solution is worse than the problem! Though I will give the pigment idea a try. Got plenty of that on hand.