I just tried double sided tape and it held great. Almost too well. The nightmare is that the tape wont come off the good piece. I used the type with the reds strings inside. It wont sand off, just gums up the sander. Can’t take it off as almost seems like rubber cement with 100 times more stickiness. Anyone have any suggestions? I’m going back to painters tape and super glue.
I use this…it holds very well and comes off clean.
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Try acetone as a solvent. I use double sided duct tape from Lowes.
Look on the tape package and see what you use to clean up any residue. It could be acetone, lacquer thinner, even alcohol or mineral spirits.
“Cant” go wrong with blue masking tape, one layer on spoil board and the other on the material.
Bond these two together using CA glue.
Plenty of holding power and release much easier when you want the tape gone 
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I use carpet tape and it works great. I can often do 3 projects using the same tape.
I had exactly that same problem. I used a two sided tape sold for holding down carpet. I haven’t used it since. Tape can be a good solution when pieces without tabs would otherwise come free. Many people have been using the blue masking tape on the spoilboard and the workpiece and gluing the two together. I haven’t tried that myself, and I wouldn’t use that for everything, but in some cases I would give it consideration.
Mostly I use T-track clamps now, but even those can have problems.