Pretty much all promos from all hotel programs that give you free nights do it by stays (which means maximizing them involves changing hotels every night or otherwise making your nights at a given hotel non-consecutive). That's in large part because too many people stay multiple nights, and they don't want give away free nights that easily. They realize that many people either won't think to "hotel hop" (the FT term for changing hotels every night), or won't bother to. And thus they can make the promo sound more lucrative than it is (for most people).

Promos that involve nights are almost always extra points, not outright free night certificates.

That sounds like a good plan, especially if the cost of the stays is not coming out of your own pocket. (In many places SPG is more expensive per night than some of the competing brands, but of course I don't know if it is where you are and I don't know if that matters to you.)

However, keep in mind that these hotel promos are not usually really "quarterly". One hotel program may have a promo that runs Sep through Jan, another might have one that runs Oct through Dec, andother might have one that runs mid-Nov through mid-Feb, etc. So don't only check what other hotel promos are 4 times a year, because you'll miss out on some of the best promos that way. Check at least monthly so that you know soon after it's announced what's coming up in each hotel program, and can then evaluate which one will work for you, and when it will work for you to switch (if you find two promos from two different hotel programs interesting but they overlap in time, you'll have to decide how to handle the overlap, ie, whether you stay with the first promo till it ends, start on the second promo as soon it starts, or something in between).