Counterflow chiller options - kettle has no spigot

The problem is probably not the air temp outside. It's probably the temp of your water. The easiest way to solve that (IMO) is to add a pump to recirculate ice water through the immersion chiller.

My water temp is currently 71F. Without making the water colder, there's no way any type of chiller could get the wort temp below 71F.

 

Weldless ball valves are easy and inexpensive to install in aluminum. Also, if (when) you move up to a larger pot later, the valve can be installed on the new pot. Go with the stainless ball valve and take care of it. It will last a long time. Also, while stirring the wort while chilling won't get it to cool lower than the input water, it will cool MUCH faster if it is being stirred (and stir in the opposite direction of the water flowing through the immersion chiller).

Here is an example.
http://morebeer.com/products/weldless-spigot-stainless.html

 

Stirring is way quicker than not stirring. However, if you are already stirring, it will not be nearly as big a difference by just switching directions. Once you get below 100-120ish degrees, you can drop a small sump pump into a 5 gal bucket of ice water to pump the ice water through the chiller then direct the output water back nto the bucket and use it as a closed chilling system.

 

You could also buy or build a much smaller immersion chiller to use as a pre-chiller, just put it in an ice bath and hook it up to your original chiller to get colder water going through your wort.

 

I used to do this. Then I figured out that a pump was more efficient, and cheaper than the second chiller (which has now been retired).

 

Of course if you are going to use a pump, then you might as well step up to a CFC or plate chiller and have the increased ability to whirlpool, brew lagers, and 10 gal batches.