You'd not necessarily see anything growing if it were fungus, because moulds/ mildew only make spots on the surface of the wood. I did have one more thought - you could, with care, shove a clean feather down the windway, so from the tip of the instrument down the hole you breath into, towards the little window on the front of the head. If you do that, be careful not to take it as far as the very delicate blade of wood which vibrates and makes the sound, but it may well help. A stiff but smallish flight primary feather would be good for that - the blunter secondaries would be a bit too floppy to manage much cleaning.
Tim Cranmore warns about block removal: there are about three different block profiles, and some are harder to remove, others to get back in again after....and he's had them stick halfway too, risking splitting the recorder head whether attempting to shove it out altogether or shove it back again to where it lives. So again, a technique best practised on an instrument which doesn't matter.
Sounds as if your treble will be made of maple - it's probably one of the easier woods to work, and some experience problems with warping and distortion of maple, but my first proper recorder was made of it and still works perfectly well after twenty three years

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