The UTH instructions also say to not put them on plastic, but us tub users have no problems.
Please don't use tape, it's an accident waiting to happen. Glue guns are $5 at any Walmart or Target.
You may need a second UTH or a heat lamp to raise the ambient temp. That's why I love tubs - no such thing as ambient temps because there's no unneeded empty space. You could try to switch to tubs?