When pushing down sims from lower divisions, doing it quickly is important. As mentioned above, sims spend some kinda effort (how much is always debated) every cycle that they are still in the game. The object is to get them down to very low. Once that is done they will effectively die off. There are SOME occasions where the sim will die off at Low. But it's detailed. And fact of the matter is, you're never safe until they are pushed to very low.
so the faster you can get it done the better. You'll have to get a feel for it. But I think the best way is to unlock the ship as soon as possible (obviously) and then do your promises. Use the offer of promises as a range finder. If your promises move the sim down to moderate, it's a sign that you're not terribly far away from pushing them to very low. Next cycle you can add your 3-10 HV, depending on all factors.... preferences, prestige, etc. BUT..... if you offer promises and the sim is still at very high or high, that tells you that you'll need to spend a lot in that cycle, or decide to move on.
But the quicker the better. Let's just guess that sim offers 2 HV per cycle (that's a random guess!). If you're unable to push sim down to very low with your initial offer of visits, the sim will offer 2 more HV next cycle. Making it more difficult to push them down now. Make sense?