I wouldn't call myself an real engineer, or indeed, any kind of engineer but...

That sound like a good plan to me :)

Ross, What's the end of the quill look like? e.g. does it have a centre spot from the taper machining operation?

The accuracy depends on how square the chuck was to the quill initially...
Actually, your clever plan means the new drill 'chuck' will be properly aligned with the quill travel regardless of vice alignment.