I know there is lots of tape out there, but my need is specific...

I do a lot of vector-cut 1/16" and 1/8" acrylic lettering and have always hand-cut and taped the backs with a strong double-stick tape (between 1/8" and 3/4" wide). For obvious reasons this is time consuming and somewhat of a chore, even though I've become a very good taper in the process! I've never been taught a better way, so I'm hoping someone here can suggest something better.

I'm assuming there is a strong double-sided tape (preferably wide) I could apply to one side of the acrylic, then vector-cut, and then just peel the other side of the tape and apply. It needs to be strong tape and leave a clean vector cut on that side of the acrylic.

Is there any product or technique you guys can recommend? Much appreciated!