So, I got into PF and quickly beat all levels 1-14. Then in Level 15, there's that annoying cannon that snipes your HQ every 2 shots it takes, causing it to jump out and force you to go without power for 20 seconds. No other ship gets 1-shotted like that (unless it's damaged). I think the giant gun should actively avoid aiming at your HQ, or it should make a gap in its shots to give defenses time to rescue HQ.
EDIT: Actually, no. Leaving a couple ships to defend seems to stop HQ Sniping.