| I would just measure the minimum height of your bridge, factor in string height off the fretboard, and see if you maybe don't need to add any height. Most fingerboards are only 1/4" thick or sometimes just a hair less, and 3/8" is plenty tall, especially if you are going to add frets. If the bridge gives you minimum 1/2" string clearance, then I'd think that having the fretboard 3/8" off the body should be fine.
To be sure, lay everything out - neck, bridge, fingerboard, and nut. Place a straight-edge from your nut to your bridge, and take a look at your string clearance. You'll probably want ~3/32" clearance on the low string, and ~1/16", give or take (depends on your personal preference, of course).
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