Most WW2 planes used centrifugal superchargers, more closely related to the Turbo - not positive displacement Rootes type superchargers as the LSJ does.
The centrifugal blower has the same issues though, it is related to engine speed, not engine needs.
... at sea level.
At 5000 feet it will be 220hp and at 10,000 feet it will be 180hp, a fact of physics that can not be changed unless you have the ability to de-couple the blower from the engine and increase it's speed to compensate for the altitude change ... A turbocharger does this automatically.
... and the reason I suggest a turbo to overcome this issue is not because I am talking "one on one" with you, but because this is an open forum topic that thousands of forum visitors are reading of who some might choose to follow a different LSJ path to you and informing people that the choice of a turbo to maintain boost pressure at altitude is very relevant and very on topic to this thread.
If you do not wish for posts like mine to appear debating or questioning your choices then there is a closed section where you can control what is posted ...
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Interesting project none ever the less, good luck with it all.