Okay, finally got it to work the way I want it to.
I changed code in admin.googlesearch.php to allow for the full google id. Line 43 was changed to:
if (trim($_POST['google_id'])!='' && !preg_match('/^\d{16}:\w/', $_POST['google_id'])) {
This allows for the 16 digits followed by a colon followed by the alpha-numeric string. This of course required the database field size to be changed to 28 from 16. There were a couple of other spots in files that were also changed from 16 to 28 but I'd have to hunt those down again.
To get multiple sites to be searched, I set up the sites in the Google Adsense Custom code on the Google website (thus the need for the full partner-pub #). In googlesearch.lib.php, commented out lines 175-182 (before "else" but after "{" and after the "}").
I think that was pretty much all - rough but it works :) Not sure how it functions with two Joomla sites - one of mine is Joomla, the other isn't - so there may be other changes required for that situation.
kksou, I can bundle the files and send them to you if you would like for reference.
edit: To view it in action, check it out at
http://www.thisweeklive.com/index.php?option=com_googlesearch&Itemid=1819
My general manager is EXTREMELY happy with the result.