Didn't you say you have a fermentation chamber that is temp controlled? If so, you could put the fermenter in there and allow that to bring the temps down even faster after your ice bath.
A good wort chiller (immersion) shouldn't cost any more than 50 bucks or so and xmas is coming. I have been using the same chiller since when I first started 12 years ago and believe me I do not have any thing close to a "pimp my" section that I would ever post anywhere for anyone to "drool" over.
I still brew on the very first all grain cooler I got years ago and about the only upgrades I have made are 3 temp controlled fridges/freezers for storing, serving, and fermenting beer. I brew very hands on and have simple equipment. I do my best to pay very close attention to yeast handling, sanitation and cleaning, as well as controlling fermentation and minimizing oxygen pickup at every step of the way. While my beers come out good, I am always trying to make them great by working with my water profiles and focusing on mash pH.
Anywhooo....you definitely don't need fancy equipment to make great beer. Keep posting and reading posts on here as well as checking out magazines like BYO and Zymurgy. These are all great ways to get better at the hobby. Keep brewing hard!
PS- Keep us posted on how this one turns out.