I thought a little more about your question and your goals. Specifically for your goals, I don't think you should spend the money on the ab pavelizer, although reading hard style abs would still be worthwhile just for the principles.
1) Lose belly fat
2) Really make my core strong
1) Is going to be about diet and expending energy. The swings in S&S will help here.
2) Hardstyle planks will really carry over into everything else you do with kettlebells and will strengthen your core in the way its used in kettelbell training: rigid and locked out, protecting the spine and providing a stable center to move from. 10 reps of 10 seconds each will give you an idea of the power of these planks. They aren't like the 60 second planks you may be familiar with.
Straight leg sit ups is the cheaper alternative you asked about. You can add weight, too. Keep your heals on the ground throughout. The ab-strength will carry over into your getups, even though the getup is more a side roll than a situp.
Should save some $, which you can spend on a session with an SFG to get you going.