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I Think this is the right way to do it. I have one suggestion. If you have an identity safe profile with passwords saved, take a backup of them and then run the Norton Removal tool.
I would make sure to have some AV/Firewall active while installing SP3. Even with very high-speed, the active internet connection is a long one; and there is no reason to leave yourself vulnerable during this time.
I have installed SP3 on a couple of dozen client's machines by now. Everyone had an active AV/Firewall at the time (most of them Norton products); none of the installations had any problems whatsoever.
I have NOT tried installing NIS 2009 before installing SP3. My preferred order has been:
KEEP the 2008 Norton product while I INSTALL Windows XP SP3
THEN INSTALL the Norton product by either
a. Installing NIS 2009 directly (my choice and I've had no problems); or
b. Uninstalling the 2008 product using ADD/REMOVE Programs (the method recommended by others here) then installing NIS 2009.
Important Note: If you have NO OTHER NORTON PRODUCTS, you should also remove Live Update prior to installing NIS 2009.