Taking off the string and measuring the ball end to start of taper is the definitive approach for string through and other varieties of out of the ordinary string anchorage. No longer guess work. Bob's your uncle, Charlie's your auntOne thing you could do is lay an old bass string onto the currently-installed low E, all the way around the, uh, cylinder? and up (back?) to the tuning post. Then take it off, straighten, measure with the stiff tape.
The reason why I ask is to ascertain the chance long-scale strings fit. Which would open up a faaar wider range of options.