Greetings:
Thank you for clearing most of that up.
I now recognise what they are and what they do. I have seen them frequently.
Whether these TABs can be re-used seems to primarily depend on the integrity of the traces on the flex substrate AND the LCD glass, after the removal and "cleaning" has been done; if trace conduction is poor, you may need to repair it (them) with some kind of conductive ink, and hope it survives the further handling and bonding steps.
An "INK" I seem to recall seeing, recently, used for "printing" circuits on many substrates, was a two-stage system of two relatively available reagents, one a compound of silver ions, the other that converted the first to silver metal.
ISTR, they used it in an ink-jet printer, different tanks, and could print usable circuitry on even paper or cloth, using many passes. Fill two Rapidograph pens, wait between stages, retrace, and you may have something usable. YMMV
I also saw something about alloying Gallium metal and something else (metal?), and drawing traces on many substrates, but I don't know how it was "fixed" to prevent smearing.
AFTER you have reliable traces, the next challenge is bonding, without shorts or opens, that will survive handling. If you can get a supplier to provide a Thermosetting/UVcured conductive adhesive, or find a sufficiently low-temperature alloy paste to bond the LCD traces to the flex traces (bearing in mind the almost-certain differences in Thermal-coefficient-of-expansion between glass and plastic substrate, which can generate ENORMOUS shear forces) you may be getting toward your goal.
NEXT, is, how do you plan to APPLY the adherent agent in a fine pattern, thin enough to not "mush" over and create shorts, but enough to make reliable connections/bonds? Silk screen/stencil is good, if Volume justifies, but hand application is cheaper for low-volume.
You said nothing about the initial condition (pre- and post- "cleaning", as to whether is enough residual, re-usable bonding/conductive material to reasonably expect a second try to work: I have assumed in the above that there is not; correct me if I err.
I don't want to try to kill your "buzz" of finding a refurbishment process of your own, and make it profitable, but I want to make you aware that Engineering, especially Manufacturing, is full of "Traps for Young Players", and the road can be very treacherous if you don't make the right turnings.
Engineering is Hard.
I hope I have helped: Or I can try again, if I missed something.

Cheers,
Dave
P.S.
I just watched the video, and one after that, about Anisotropic-conductive-films, so if your LCD/flex circuit have clean and good traces, I can see no hindrance to re-use, assuming clean surfaces.
Do you have a supplier of this Epoxide tape? If so, you may have a winner!

Sorry I jumped before I looked.
I would just advise absolute flatness of contact (within the compressibility of the virgin tape, and watch repeatability of temps and clamping force to prevent cracking of glass.
D.