Passive (energy harvesting) tag / transponder chipset solution with 12 inches range?
The easiest way to achieve higher ranges is to increase the size of the antenna. But I don't think that such a large distance is possible with 134.2 kHz and a reasonable sized antenna.
Another possibility is to increase the frequency but still remaining inductive coupling. UHF-RFID (860-960 MHz) would be great for range but terrible for energy harvesting because there is electromagnetic coupling and no inductive.
HF (13.56 MHz) seems to be a good solution. You already mentioned the possibility to move towards another standard like ISO/IEC 14443. But if you want to switch to 13.56 MHz, you should use ISO/IEC 15693 because the minimum required field strength is much lower. The maximum range is up to 1 m, which is suitable for your application.
One more note. The communication from tag to reader is done by load modulation. A relatively new chip from NXP (NTAG 5 boost) uses active load modulation. NXP claims to achieve the same read range like passive load modulation but with a 40 times smaller antenna. Conversely, with the same antenna size, the range with active load modulation should be significantly greater than with passive. There may also be solutions from other manufacturers that I am not aware of.
In summary, I would recommend using ISO/IEC 15693 and maybe consider a chip with active load modulation or similar.