It doesn’t matter either way if he’s got them and you don’t you’re going to lose. Therefore the purchase of AA guns is irrelevent. Obviously if you’ve developed Heavies and have some extra cash then AA’s can be bought, but remember that someone with Heavies is likely going to target your factories so that you cannot develop this tech yourself. Once he can eliminate that threat the game is over. In other words you need to develop tech while you still can.
There are a couple of things I think you are overlooking which should apply to any ruleset even your house rules. First, in A+A defense is much stronger than offense so for this reason an offensive campaign has a much higher level to reach to be feasible. Secondly, the game as is was not unbalanced because of some minor rule or procedural incontigruities but because of a severe material shortcoming for the Axis in terms of force on the ground at the start of the game. The Allies can too easily remove too much too early so that no matter what rule changes you want to affect it isn’t going to solve this. Thirdly, transporting troops is effective because it is possible for the Allies to use Russian space that is put their troops into Karelia to help defend there. Some house rules don’t allow this but even so this doesn’t deter a “shucking” strategy of men from the US and Uk to Europe. Instead the focus will shift from Karelia to WEuro, a little less ideal but certainly still workable. Ultimately, the Axis as the protagonist cannot afford to spend many ipcs on innanimate objects like transports or factories, both do nothing but produce real units so unless there is a dire need for this as in the case of Japan it is best to avoid doing so as is the case for Germany.
Have never played the Hasbro version online, only against the AI, or as all 5 players usings strats from these boards.
I THINK that Hasbro’s multiplayer is direct-link, meaning you and your opponent both need to be online at the same time, and one player makes a direct IP link using the Hasbro program. Never did it before, so cannot be certain.