Here's another update, and this is probably going to be the final word!
I had got the ANTS Load recording proxy to work with IE7 by changing the 'HTTP/1.1 through proxies' setting, but this was not 100% reliable. It seemed to work sometimes, and sometimes not, as did changing the security settings to low.
It seems that Microsoft had hard-coded some restrictions into .NET Framework, so that when this is installed in conjunction with IE7, IE will no longer connect to proxies with an address of localhost. I got this information from the Fiddler website, which uses a similar technology to capture HTTP traffic. Here is a reference to that website:
The workaround, which also seems to work flawlessly with ANTS Load's script recorder, is to use the local machine name instead of localhost, when recording a script against a website hosted on the local machine. for instance, instead of