You can climb on a boat overloaded no problem. The position is a bit tricky, you need to be lined up and not too close to be under it.

Just FYI if you are almost out of stamina you can just log out and back in to get full stamina back. I wouldn't use it normally but this kind of thing is just a cheap death due to awkward mechanics. Considering the skill loss penalty I'd rather do that than eat the loss due to a cheap death.