It's less the nut to tuner spacing as the string construction. You want the low E string's outer wrap to finish just after it goes over the nut, so that only the thinner inner core goes around the tuner post, especially as you have guitar tuners rather than larger post diameter bass tuners. You don't want the thick wrap to bend around the small radius of the tuner post as it won't do the string any good.

Hopefully dedicated Bass VI strings should take that into account.