Yes you can
Pregame write out a mission / tactic / objective for each nation. Then refer to it each turn turn to keep you honest.
Germany could be complete sea lion
Japan could be conquer China and India
Etc etc
Tanks don’t have to be adjacent to their attacking territory either. They can move 2 spaces to attack. For example, say you have a tank in Germany and you are attacking Baltic states. You can move through Poland with your tank and attack Baltic States.
I agree with you on heavy bombers. Classic version were OP - basically, I win buttons since they threw 3 dice each (3@4 for 12 IPC vs any other build was a bit much!) However, 2 dice and keep both results for combat is fine. I draw the line at for SBR, maybe 1d6+2 or best of 2d6+1 there.
First time I did a custom map that’s exactly what I did, buy a world map and territory borders. You could try to find an loder copy of photoshop like ps 6 or 7 for much less than the current gen.