Tape adhesives will normally begin to loose strength at higher temps. You could try a heat gun, or better yet an oven to bring the parts up to 160 to 180 deg F. Such an oven could be made from light bulbs in an insulated box.

Drag knife applications will be extremely sensitive to material flatness. It is frequently important to surface your table frequently to ensure it is true to the spindle. Vacuum hold down is very important. That being said a vinyl plotter can be obtained for very little these days ($250 for 31in width on amazon) and cuts vinyl more efficiently than a cnc router. Signs like this are applied with a transfer tape, so it is very easy to locate accutately without different components moving. Stencil materials are available as well.