Protecting two layers of PCB with electric tape?
Kapton tape is a widely available industry standard product for this scenario. You can view the specs here - from table 3 you can see that it has a dielectric strength of over 100kV/mm, plenty strong enough for your purposes. It comes in different thicknesses but any standard 'off the shelf' kapton tape will suffice.

I'd recommend it over electrical tape as electrical tape tends to leave a sticky residue and is thicker, which may be undesirable given your height restrictions.