I would say your chances are reasonable, but not great, because of the very narrow window that you’ll accept. Week 35 (9/1-8) is the first week of summer-end Gold season at GO and likely one of the two most in-demand Gold weeks at GO. I don't think there are many owners that exchange that week, at least based on reports here and at GO owner meetings. Week 35 is not such a peak Gold week at OW (because there are two August weeks included in Gold season), so I'm guessing that you'll have a better chance there.
There will be some weeks available for exchange then, so it all depends on where you stand on the pecking order as to the strength of your week. That means making your request with the very best week you can. Assuming "NY" means a New Year's week for 2006, you should make your request now. Your trading power is maximized by depositing (or using request-first) as early as possible, preferably a full year in advance of the date for your home resort week. Thus, you should have already deposited your week. Do it today.
Normally, it doesn't matter whether you use deposit-first or request-first in getting a successful exchange. However, in this case, you should use deposit-first, because it's quite likely that your own 2006 week would expire before the exchange is confirmed.