Has anyone attempted to modernize the 7.62.39 cartridge?  Kalashnikov himself was for this rather than 5.45 or adopting 5.56.  While I am no gunsmith and no little or nothing of reloading is it possible to make the round better (accuracy, velocity, terminal ballistics) without making a new calibre and rifle?

No disrespect ment but Kalnishkov is old and thinks old like he is still fighting WWII.
Any improvment would require a larger case to get more velosity and a longer bullet with a hollow cavity in the nose so the bullet would become unstable quicker. The impoved 7.62x39mm cartridge wouldn't fit in a AKM as it would be too long and require a new designed larger/heavier rifle.
The reason the Russians went with the smaller caliber 5.45x39mm is it has it fits in the AKM size/weight rifle and has the higher velosity with a longer bullet that becomes unstable quickly.
Added to this is the lighter recoil and ability to carry more rounds per pound.