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I don't think you'll be able to get away with putting a redirect on the page either. The problem is, any true 301 redirect is going to get executed before any of the page content gets delivered, even if it's located on the page itself.
I would switch to a host that provides log file access - that way you can see what happens.
I guess I'm not sure why you think a hosted web counter solution is better than reading your own logs. In terms of giving you information on where users are coming from and what pages they visit, you should be able to get that from your logs the same way you would from a JS page tracker.
Typically JS page counters are used when your web host can't or won't provide you with raw logs that include referer information. The other thing that they can do is provide some additional information, such as screen size and window size, that you won't find in a logfile. The will show you hits to your 301 redirected pages.
OK. we better end this OT thread now. Thanks for all your help.