Whoops sorry, I just tend to assume in these forums....
You don't need to remove the 3/8" just 3/16"; say 5mm. You only need to remove the amount needed to bring the 12th fret towards the bridge, that should bring the saddles within range; there's no reason why the saddles should be right at the end of their screws if you do this.
All you are doing is contracting the scale from the fixed point of the bridge. If the scale is 3/8" shorter then the nut moves by that much, the 12th fret by half that (3/16), the 19th fret by 1/8 and so on...
There should be no need to adjust the saddles at all, if they were correctly positioned before.
If you want to improve their range, try nudging the bridge plate a couple of mm forward, or fit extended screws
Try this: measure the distance from the club end of the neck to the 12th fret, then subtract this from the 12.375" that represents the distance from the saddles at their furthest reach forward. Measure the resulting distance forward from the sounding point of the saddles wound to the end of their range and mark the position of the end of the neck on the body.
As the saddles only have to come back to compensate intonation this should give you an idea of the optimum position of the neck pocket. No guesswork.