That does seem like an abuse of the system. Perhaps the countdown to abandonment should, rather than resetting upon resubbing, start counting up (after maybe 15 days or so).
So I drop sub for 89 days -> eat a dac -> timer stays at 1 day until abandonment for 15 days, then starts counting in reverse (so you'll have 16 days when your 1 month expires to get a new sub). Won't have much of an effect on normal gameplay, especially if you're subbed for 3 months at a time and actively playing, but will keep HQ alt spammers from being able to cheaply hold tiles.