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I can't answer your specific question as to the 13' but I do know a rope ladder type won't work.
You have a pretty small free-board and transom therefore when using a rope type ladder your feet will disappear under the boat causing you not being able to step up with out tremendous upper body strength.
Therefore you need to find a ladder that is straight and sturdy that stands of with some kind of support at the lowest point possible on the boat.
Hopefully somebody here has a ladder on their 13' and can chime in.
Have fun.