Glad you have been enjoying the game so well.
Regarding feeling rushed, that really shouldn't be the case. AI War really lets you set your own pace, and in fact I am like you and tend to want to play a much more relaxed, thoughtful game. If you are playing on maps of any decent size (40+ planets), you should not have to feel rushed. Honestly, if you want to have a more relaxed game one good tip is to play 80 planets or 100 planets. That gives way more room to expand, and you are less likely to be next to targets that you don't want to have on alert when you are making strategic captures, etc. Originally at release the game only supported 80-120 planets, but players were clamoring for smaller, faster-paced games, so here they are.
Regarding reinforcements, your goal is simply to make sure that the AI is reinforcing in places you don't care about. If all the on-alert planets are planets you aren't planning to take, that's the best. Then they are just forming a "crust" of massive defenses around you, but everything further out -- that you really care about -- is completely unaffected unless you leave it for just hours and hours. And even then it is still winnable, but it just gets more grindy. If you use transports to jump past the crust, then you're really easily bypassing that and it's not really doing you any harm. The goal is always to take the AI by surprise on any planets you are attacking, but except on the smallest maps that in no way involves rushing on your part -- in fact, sometimes that encourages quite the opposite, since if you build up a decisive force and hit it all in one go you'll incur the fewest losses.
The game can really be played either way, and there are plenty of players here who will advocate one style of play or another. My feeling is that a lot of them prefer things a bit faster than I do, and so a lot of the strategy discussion reflects that, I think. But when I was designing this game, one of the specific things I was wanting was a game where you never had to feel rushed -- and that's a big part of why I came up with the AI Progress mechanic in the first place, actually.
Hope that helps!