Trump's solution? Cut the U.S. corporate tax rate to 15% from the current top rate of 35%. This would make corporate inversion unnecessary. I think he also had the idea of capping tax at 10% for companies wanting to bring their money back.
At some point you have to ask yourself "why are companies doing this?" and fix the root cause.
Creating a race to the bottom is the opposite of fixing the root cause. The US already has a way to deal with this as it's the system used internally between states: levy taxes where sales happen.
Do any presidents actually follow through with what they say during pre-election? Plus a president doesn't even have the power to lower corporate tax by himself anyway.
At some point you have to ask yourself "why are companies doing this?" and fix the root cause.