Spock, it's really quite simple so you're most likely over thinking it 
The two scenarios are similar in that they both remove the possibility to choose otherwise.
Mr. White's device removes the possibility of voting republican. Likewise God's omniscience removes the possibility of voting republican (if He foreknew that you would vote democrat).
Since, in Frankfurt's scenario, Donald votes democrat of his own free will without the device being activated, we realize that free choices can be made in the absence of multiple choices. Therefore, God's omniscience of our future choices doesn't remove free will.

The two scenarios are similar in that they both remove the possibility to choose otherwise.
Mr. White's device removes the possibility of voting republican. Likewise God's omniscience removes the possibility of voting republican (if He foreknew that you would vote democrat).
Since, in Frankfurt's scenario, Donald votes democrat of his own free will without the device being activated, we realize that free choices can be made in the absence of multiple choices. Therefore, God's omniscience of our future choices doesn't remove free will.