Would longer axle to crown be ok?
You should not try to adjust your riding position by messing with the steering geometry. Riding position should be adjusted by replacing the stem with one that is longer or shorter of has more or less rise.

However, it sounds like you need a longer fork anyway. 375 mm axle-crown sounds far too short. I put a rigid fork on a 90's 26" wheel MTB that only had 40 or 50mm travel and the axle-crown was 420mm. I suspect you have steepened the head tube angle too much which is why the bike steering is too fast.

It's possible to make an estimate of the crown-axle measurement of the original fork by making some relative measurements on a high resolution image of the bike knowing the rim diameter is 559mm. The Trek archive page of the 2014 820 is here which provides just that. I estimate the axle-crown is is more like 460mm.