Downsizing the warhead increased the range, quite a bit. If you have an atomic or chemical warhead that weighs less then 450lb, then you can throw it farther. GPS means that accuracy doesn't suffer..much anyway.
GPS is not that easy to spoof or even jam, and you'd mess up your own systems too. They are probably using GLONASS, the Russian version of GPS, along with our GPS, and if you turned ours off entirely, they'd probably revert to GLONASS.
As to how we know they are using GPS.. well a little birdie probably told us. And I'm not speculating on which sort of birdie that might have been.
Probably Russian supplied GPS units.,...or Chinese.,...