Would it work if I were to tape it to the inside roof?
That would be less efficent and probally wouldn't give you the basking temps required.
The best solution often is to cut out a section of the floor for the heat tape than cover the entire floor in a durable material, suc as PVC.
You could could sandwhich the heat tape between a material and the floor but this can be disaterous as the tape needs to have a gap to allow air to flow or the heat will build up until either the tape melts and fails or you ignite the cage.
I personally have my heat tape in the walls of my enclosures and on the back sandwhiched between reflectix material and not sealed to allow airflow and expansion.
Best of Luck

-----
Jeremy
"I am become death, the destroyer of worlds" July 16, 1945 Robert Oppenheimer
1.1 Double Het "Sharp" Snow RTB's
1.1 Hypomelenistic RTB's
0.2 Pastel Hypo RTB's
2.0 Double Het Stripe Albino RTB's
0.1 Suriname RTB
0.1 Anerthrystic RTB
0.0.10 Red Bearded Dragons
1.1 Rhinoceros Iguana's
1.0 Green Iguana
1.0 Ball Python
1.1 Cream Golden Retrieviers
1.0 Pomeriaian
0.2 Catus Terribilis
0.1 Spouse
1.0 Child