When I am not using this game to introduce new players, we always use low luck dice mod and/or the units from 1940. Not just artillery, but everything, cruisers, AA, etc.
This game is meant to be quick. Usually when we are short on game time we play this one with low luck because low luck eleiminates a lot of time-consumming dice rolling.
The whole style of this version is not for hardcore strategists. There is only so much to do and too many cases of “optimal” moves that everybody more or less should make. Sometimes just playing this one casually as a social game can be a lot of fun when crazy luck results in weird games. An example:
I remember one game in which Russia totally killed Germany, while Japan had managed to get all the way to the US. Berlin and Washington fell. The UK was left in a dismal situation with Australia and India captured and a Japanese fleet in the Atlantic itching for a London victory. I never though the Axis could win with London and Washington and NOT Moscow, but if it were not for smart UK play, this might have happened. Alternatively, Japan liberated Berlin, but it could not hold. Meanwhile, in China and the Middle East Russia and Japan were fighting it out hard. With its mainland factories, Russia eventually pushed the Japenese back and got India and Africa for the UK. Japan surrendered holding the Pacific islands and North America.
Games like that were fun, only spurred on by poor play (by new players) and crazy luck that made their poor play actually come through for victory.
If you really want to play 1941 as a strategist, you need to make big changes or use a luck-reducing way of play.