Hmmm, that won't work for this particular project, but it is really good advice for the future! I will keep it in mind.
I tried an experiment last night: I stamped my image in Brilliance ink onto a clear, glossy transparency yesterday and let it sit overnight. This morning it is permanent and won't smear or rub off, so I am hopeful that the Brilliance ink will also dry and remain permanent on the plastic. I stamped it this morning and will see how it looks tomorrow - I'll keep you posted! Thanks ladies-