I hate being the odd man out here. Can I try again?

I am afraid that putting tape on the back of the plastic meant to be inserted into the bottom track would 1. leave a gap at the top or bottom of the cove 2. the plastic would make it difficult to work with and the tape would never hold it in place.

You might consider these options. Exchange the cove for the type with the sticky back. They have a peel off strip just like double sided tape, but this stuff is real sticky. This type of cove is easy to work with also.

Is it possible to remove the plastic from the back of the cove before you install the tape? The cove that is made of styrafoam with the plastic glued on should adapt well to this. The hard molded plastic cove may not.

Just a couple more ideas, Dennis