The tape probably would stick better to the Aluminum bed than the BuildTak clone sheet you have as it would have had more surface area to bond to.
What I found that works best is to print on the bare aluminum bed using a PVA based spray, this can be hairspray or a specific 3D printer product like 3DLAC, or just glue stick. I ditched tape after day one (for reasons you mention) and solely print on aluminium or on glass without a problem, sometimes it sticks too well and the bed needs to cool down to room temperature before I can remove the print. This has been described as an answer to: Should you use hairspray on a metal bed 3D printer?
Removing the BuildTak clone sheet may be quite laborious if a very sticky adhesive is used (it took me a long time and lots of solvents to remove the goo/glue from a PEI sheet I used once) it is better to try and print on the BuildTak sheet, maybe use PVA based (hair)spray or glue stick.
Furthermore, ABS is more difficult to print than PLA or PETG. Printing ABS is difficult because of the relative large shrinkage when the filament cools. It therefore requires careful heat management (no part cooling, no draft, enclosure, etc.). This filament needs a good surface to build on and requires brims, "mouse ears", adhesive spray or glue to get the first layer to stick and not curl up. Tape at temperatures of 100 °C will become soft and loose its power to stick. Kapton tape might work better.