If you value your free time at all, you simply buy 1,000 points for $24. The points themselves are worth $15-20, so really you're just burning $4-9 to avoid wasting time with other strategies to get a few Hyatt points.

And FWIW, if you are a member of one of the cashback websites, you will get cashback on points.com purchases. Topcashback for example frequently sends me a "spend $10 and get a bonus $10" offer, so I can bring my per-point cost down to a very attractive level, even when paying regular price.