That's plenty for those fatties. If you follow the 37mm line on Berto or Heine's charts you'll get about 50/60psi and if there were a 40mm line it would be lower. Berto's writeup also has a MTB section which kind of implies you should be in the forties.
FWIW my 37-622 aka 700x35c size measure about 36mm wide on rims that are 16/19mm inside/outside.
Is the squeak constant or does it happen at a certain point during the rotation?
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Genesis 49:16-17
"Well, well!" said Holmes, impatiently. "A good cyclist does not need a high road. The moor is intersected with paths and the moon is at the full."