Air shows and museums booths are OK in the crowd they target, but they give you a very VERY limited exposure. The TV ads also reach a very small crowd, American only.
AH needs internet exposure because this turns to the international global masses. AH has next to zero presence on gaming sites. If you grab some random teenager and ask him to find a WWII flight simulator for you, it is very unlikely that he will come up with AH. There are all the chances that he will come up with IL2 or even war thunder, and the latter is not even released yet. Even on specialized websites such as simHQ.com where I first heard about AH 12 years ago, you will be hard pressed to find any mention of AH.
AH must appear on major gaming sites such as gamespot as a premier flight simulator/ air combat game. More specific MMO and war gaming sites are also good. First stage is to get it listed there. In some of the site AH is listed, it looks like a dead game - no reviews, no news items, no promotion trailers. I bet it is not very difficult or expensive to create news items and distribute them to these websites. Every patch and development announcement should appear there in a big hu-ha. A new trailer every time a new plane/vehicle is released will go a long way. This constantly bumps AH up the news items list and make the game page on these websites looks alive. Dev interviews can work with some websites.
Second, AH needs some invited reviews from these websites. Still cheap. No official reviews makes it look like an insignificant second-rate game. Reviews bump you up the lists and makes you visible on these websites, regardless of the score you get.
Last, ads and banners. This does cost money and I suspect that on some websites it costs a lot of money, so a more targeted approach is required, probably going for smaller sim/war gaming websites. If AH can have some "special offer" to go along with that (a free month instead of 2 weeks, chance to win something etc.) it will be much more effective, but that means money again.