If you have problem with GM cars, your best bet is to check their TSBs. There're like a billion of them out there, almost all have them have similar problems (wonder why?

). You can usually find the source of the problem with a simple search. I found out about a loose connection problem on mine couple of months ago, that saved myself a pricy tranny job.
http://www.alldata.com/TSB/48/994826F7.html
http://www.alldata.com/TSB/48/994826GK.html
Not sure if the tires are really the problem, it's possible though. I know for some N body cars, there was a problem with the goodyear eagle LS/RS-A. Basically they had to replace the tires with a newer revision in order to get rid of the noise. Don't have the TSB handy but you should be able to find it easily.