Quick answers:
1. The AVID Assistant app addresses all of your speed-of-play and difficulty issues, especially if it makes it to the stretch goal for full vector movement plotting. Hopefully, folks have read the stuff about the app and can see exactly how that works. (Web version of the app will be free to anyone.)
2. Squadron Strike is structurally much, much faster.
So, those are sort of backwards from the order I wanted to write about them because it makes more sense if I explain the overall speed issue first, and then explain about the app. But, the Kickstarter is about the app, so pointing out that the app is the solution is really the point, so ... I think I was in danger of writing myself into circles.
In Squadron Strike, two modestly experienced players flying four ships each can finish turns in 10-20 minutes. Longer turns are the ones with lots of shooting, just because damage allocation is more detailed than in Full Thrust, say. (It's a really clever system, so it moves way faster than you'd expect, thanks to the design of the ship sheets.) Each point of damage goes to a particular system, instead of knocking off hull points or hit points.
So, what makes Squadron Strike much faster than Attack Vector: Tactical?
AV:T used segmented movement, and segmented everything. Eight segments per turn, and in each you had to decide if you were thrusting or not, what your thrust was, whether you were starting a pivot and/or roll, and whether you were firing. So, not just, "OK, I move my one hex for segment 4," but more of a complete turn procedure each segment. You also had to record the thrust dots you were building up, move the ships on the map, update the AVID if you were performing a pivot/roll and your orientation changed this segment, record power generation, etc.. Yeah, rolls were segmented, so you might or might not do a small pivot on a particular segment (all of the small pivots would add up to the complete pivot that you plotted).
Squadron Strike takes that whole 8 segment turn and just does it as a single turn. That means that you don't have to worry about segment-by-segment pivots and updating all of the marks on the AVID every segment or two. Instead, you're just deciding where you're going to be pointed at the end of the turn and that's it. Thrust, you just take all of the thrust that you would accumulate during an 8 segment turn and apply it all at once. Boom. Aside from all of the mechanical ways that things speed up, you only make decisions once per turn instead of 8 times per turn. That's a huge difference.