US reaction to German West Indies post Venezuela Crisis (early 20th century)

Backround:
In 1907 Denmark finally recognized the northern Schleswig border (https://de.wikipedia.org/wiki/Optantenvertrag) basically giving up their claim to a referendum in Northern Schleswig which had been promised in 1866 (Treaty of Prague).

What if through changed circumstances Denmark doesn’t back down and Germany is pressured by Russia and/or the UK to hold such a referendum.
Denmark (supported by Russia and/or UK ) wants a referendum just north of the modern OTL border (knowing this is where their chances are best)
Germany in return offers to hold a referendum in all of Schleswig (which they are sure they would win)

Imperial Germany negotiates with Denmark and in exchange for the sale of the Danish West Indies they agree to hold a referendum, but split northern Schleswig into two voting zones.
On one side Rødding,Haderslev, Toftlund, Skaerbaek, Romo and Løgumkloster.
On the other Flensburg, Tondern, Aabenraa, Sonderborg, Sylt, Niebüll, Leck and Gelting.
This basically secures them both a win in each zone and keeps german continental losses to mostly unimportant territory.

Question:
So now to the original question: In the above described scenario both sides (Denmark and Germany) want to exchange the Danish West Indies. The US already tried to buy the Danish West Indies in 1902, but was rejected. The monroe doctrine does to my knowledge not apply.
But the US under Teddy Roosevelt surely won’t just sit by and watch the Germans build a naval base so close to the Panama Canal? Or would it?
 
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Bumping once

If anyone is having trouble imaging/believing the background, I would be glad for any answers concerning the US and possible german caribbean colonies in the early 20th century.
 
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