Fair? This is war, who wants fair!?!?!
Seriously, LHTR is the way to go with NAs. They nerf the allies a lot, but also the axis a little.
If you want to use the rules from the box, try giving the allies 2 advantages and each axis power 2 advantages. Roll random for the allies, let the axis pick after the allied advantages have been determined.
That should seriously hamper the allies even with vastly superior advantages and give the axis a better chance.
Or, you could assign a monetary figure to each advantage. Add up all the allied advantages, subtract the axis advantages and give that much money to the axis to invest in units to place before game starts (this would be on top of any bidding you may have to begin with.)
Superfortresses may be 100 IPC
Atlantic Wall may be 30 IPC
Thus the axis here would get 70 IPC in units.
(These numbers are for demonstration only, obviously 70 IPC (+14 tanks!) would be an automatic death bell for Russia! So these would not work.)