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Well, they didn't build the boat around the cable, so it's gotta get through there somehow. They may have put some of the hoses and wires through AFTER the cable, though, so you may have to wrestle and move some of those other things a little. Definitely tie the new one to the old one and use it to pull the new one through.
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I can say that isn't the same look mine has.
Mine went thru a hole that I had to bend the rudder end almost 90 degrees to fit.
Your cutout almost looks like the square end of the cable would pull up thru instead of the back piece being pushed. But I don't know if you would have the distance between the floor and the bottom of the boat to get it
If that area is covered by another piece (such as mine was, I would be tempted to drill another hole that would fit the nut end to make it easier). (Would prob do it anyways if you can move all that out of the way for clearance).
Jigsaw, holesaw, etc where the existing cable is seems like you would have enough clearance to enlarge.