A way, green/black rubber cement and laquer thinner. If you plan on using the rim over and over. Only if the rim does not melt in laquer thinner which can happen to certain plastics. (test on a spare rim) Apply rubber cement to rim and to the inner side of the rubber, let dry. Then dunk the rim and tire horn in thinner. Quickly brush some thinner into the inner tire to get the glue slippery. Push rubber tire down over horn on to rim and seat the tire. let dry.
Ready to true in less than a hour. That's how you would do it traditionaly.
If the rim melts in laquer thinner or it is a on time shot, CA glue is the other common choice. Some people set the rim down on a suface (with wax paper or non stick surface??) push the tire on the rim dry and get it positioned. Then stick the CA bottle tip down in between and give it squeeze in circle motion on the way back out. Making a spiral of glue... I have not tried this just heard that is a way. Acetone will melt CA to get the tire back off, usually the rims that melt in the laquer thinner don't melt in the acetone.
Either way, have pleny of ventilation...
And perhaps there is just the trick that the guys using your setup have, with your particular rims. The tape may be fine...
Thanks to all the people helping with the Seatac Track Project.