If the scan app is not compatible with Win8.1 then its not compatible. HP is unlikely to do anything above any beyond what they have already done for this OS and your printer model. This printer model is several models back in that series and is likely already End of Life (aka - no more support). That means you must rely on the MS Updates for the scan drivers and 3rd party scanning applications.
Your best bet at this point is to purchase a newer printer model that has full Win8.1 support. Getting the 1312 to adapt to its new enviornment seems less and less like a viable option.