From today’s amNewYork:
tamp [tamp] – v. 1. to force in or down by repeated, rather light, strokes: He tamped the tobacco in his pipe. 2. (in blasting) to fill (a drilled hole) with earth or the like after the charge has been inserted.
No. I don’t think that works here.
Also, I don’t think most readers of amNewYork have ever even heard the word “tamp.”