FF - congrats on the draw! I, as always, have my $.02...
I took a quick glance at your link, but did not see the info about equipment rules (other than the list of 9,000 things you can't bring in). Does it specifically state you may not use sights? If not, you can mount sights on a traditional recurve, in fact most already have the inserts ready for it.
If I were doing it on short notice, since I have not shot a recurve for 7-8 years, I would emply a little trick taught to me by a devious soul. Take a wooden match stick and some tape. Tape the match stick on the bow so it looks like a sight pin. Sight in normally, only worrying about distance - not left right. Your left-right should be straight down the arrow. Once you get 20 yards figured out with the match stick, carefully mark the back of your bow with a sharpie, repeat for other yardages. I was never confident of my recurve shooting to go above 35 yards.
Only warning on this is to make sure you have the arrows set up exactly the way you are going to hunt, so you will need a broadhead target and either expect to resharpen fixed blades or replace replaceable blades (minor expense).
Are you going wood arrows or "modern". Best source I ever found for wood arrows when I was shooting soley a recurve was 3 Rivers Archery
http://www.3riversarchery.com/
They will match spines and fletch them up, cut them and install field points (and even broadheads, I think).
Last thing, especially with little time to spare, is get the lightest poundage allowed for the hunt. One idea, if you think this is more than a 1 time thing is to get a take-down recurve and then you can get different limbs later if you want to increase poundage. I shot a 70# Martin Hatfield Take-down for years and always planned on gettnig a set of lighter limbs, just never got around to it.
I love heavy pull bows as much as the next guy, but with broadhead and arrow technology, it is just not neccesary. A traditional native american bow made with traditional materials and techniques is hard to get over 30#, and it worked fine for them.
Lastly - just fling a lot of arrows before you go. I have my bow and practice arrows hanging out back where I can grab it and shoot everytime I go outside. Keeps me from finding excuses not to get it out and shoot.
Sorry - I don't have a lot to say regarding buying a bow. You could check your local pro-shop for any used deals, and I have seen shops that had a lot of hunting recurves, but more the exception than the rule. Again, it really depends on if this a one-year thing or possibly a on-again-off-again thing for several years. If you think you might do it again in the future, I would really recommend a take-down model from a reputable maker (Bear/Martin/etc). If it is not getting shot often, you can take the limbs off, get a nice compact case for it, and store it without worrying about limb damage.
Good hunting!