...My POD involves a right-wing, puppet Dutch government (in Amesterdam or The Hague) signing over control of DEI to Japan. Whether that was a lease or trade agreement, or mutual-cooperation pact is irrelevant. It was far too easy for Germany to starve, flood, imprison any Dutch gov't into signing any contract, lease, etc.
OTL Early in the war, neither the Royal Navy nor the US Navy have the strength to expel Japan from DEI.
Right, but the Dutch East Indies are
islands and the Dutch actually have warships and submarines over there. If the Dutch actually out there, running things on the ground in the Dutch East Indies, don't consider that there's legitimate authority telling them to hand things over (and preferably the head of state rubber stamping it, I would guess) they can make things very awkward for anyone who just imagines that they can sail in and take over unopposed.
At least the Vichy French regime in the Original Timeline was apparently widely accepted as the legitimate government of France in 1940 (and indeed whether acting under any kind of duress or not Pétain arguably
was the legitimate successor to Reynauld), which seems to have helped the original timeline Japanese takeover of French Indo-China when orders duly went forth from Vichy.
If there's a Dutch Head of State and government in exile, I have difficulty imagining that anyone in the Dutch East Indies is just going to roll over and do anything that someone sitting in a chair in Amsterdam with a German pistol pointed at their head says about peacefully handing over to the Japanese.
Edit:
Or does your point of departure involve the Germans actually
capturing the legitimate Dutch government and Head of State? Because if so I could see it being awkward for the Dutch East Indies to ignore orders from Holland, which look like they've been signed by the Head of State, to the effect 'Our number one favoured oil customer is now Imperial Japan, and please sell to them at very favourable rates...'