Maybe Hyatt weeks or partial weeks logically should rent by the point, it just seems they don't for whatever reason.
I would suggest that you try to check out Redweek prices to get an idea of rental rates. FYI, the 4 week nights generally "cost" the Hyatt owner 40% of the total weekly points "price," plus at some resorts, a split week cleaning fee (generally at the resorts that do not have daily housekeeping). So if you are looking at prices to get in idea of rental value, you could take the 40% of the full week rate.
For internal Hyatt exchanges, Hyatt will not always split holiday weeks more than 60 days out, so this may affect availability, depending on what week you are looking for. Also, some Hyatt resorts are nearly impossible for club members to book.
Once you figure out what would be a reasonable price, you need to find a Hyatt owner who has the points to your reservation. You could post something to the Yahoo Hyatt list (I will help you do this, pm me) or FB page. You could search TUG BBS for Hyatt owners and PM them. Or maybe contact some renters (as in "landlords") out there and see if they will book for you.
Good luck.
H