Patrick,
You are right, the equal signs are getting stripped out. You can see this in the console:
utag.data['qp.string1'];
utag.data['qp.string2'];
However you might be able to get what you need with dom.query_string. Check that out in the console:
utag.data['dom.query_string'];
Depending on what you need, you might be able to get away with something like:
utag.data['dom.query_string'].split('string1=')[1].split('&')[0];
Without knowing the specifics, it is hard to come up with the exact javaScript for your scenario. It could be something like a set data value where you have the above split going on with a condition that is looking for the existence of the qp.string1 so that you don't get any javaScript errors.
It will be possible to do what you are looking for with Tealium, just need to massage the data slightly. If you need help coming up with the exact javaScript, please reach out to your Account Manager.
Keep us posted on what you learn.
Thanks and Happy Tracking.
Bk