The proper response to this is to strengthen military forces in new NATO member states surrounding Russia, including US boots on the ground. This will make a clear line that Russia knows it cannot cross without provoking all-out war. Unfortunately Ukraine is not part of NATO.
I don't think this is unfortunate as the expansion of NATO is partially responsible for Russian aggression - they have a motivation to maintain a strong buffer. What you otherwise suggest has merit but is still risky. The U.S. is unlikely to engage Russia in war over an invasion of Latvia, for example, regardless of what the NATO agreement says. Placing U.S. troops there might change that, but the risk is that Russia considers it a bluff.