Just a quick confirmation check: A model with climbing plus that declares dodge can dodge while climbing, and otherwise use the climbing plus skill during dodge movement. A model with super-jump that declares dodge gains no special benefit from super-jump. Correct? Or have I missed something that might allow dodge-jumps?
Nope, you don't use Jump when dodging and that's explicitly the one and only thing Super Jump alters.
So the reason you can't Jump as part of a Dodge is because Jumping doesn't follow the general movement rules: over half the troopers base width is unsupported during the Jump movement. OTOH I can find no explicit reason that a trooper without can't Dodge onto a vertical surface. However, if you take the permission in Climb that it allows movement of vertical surfaces to imply that Move and other Movement Skills are only valid on horizontal surfaces (and I think you should) then this is the text from C+ that allows you to perform Dodge movement on vertical surfaces: "Climbing Plus allows the user to move along vertical surfaces as if performing a normal Movement on a horizontal surface." Superjump lacks an equivalent clause. So yeah, you can't Superjump as part of a Dodge movement.
Er...not exactly? Last bullet of Jump: Jumping movement must follow the General Movement Rules as well as the Moving and Measuring rules. The requirement of a minimum surface width of half the base diameter is in Move, not the GMR. The Important box under Climb is where we find this: Troopers cannot be deployed on a vertical surface, neither during the Deployment Phase nor during the game. Note that nothing else says you have to begin or end any movement on a horizontal surface. The game rules distinguish four general types of traversable surface along which you may declare movement: Horizontal surface (implied default) Stairs/Diagonal surfaces Ladders/Vertical surfaces Aerial “surfaces” (implied) These are outlined in the GMR section on ladders and stairs, and the wording is a bit odd in that it still relies on a construction in the negative—that Move applies unless a surface requires Climb or Jump, and stairs or ladders waive the Climb requirement for diagonal and vertical surfaces respectively—but it also relies on player common sense and reading the GMR, Move, Climb, and Jump like one big rule. Notably, Move and Climb require you to maintain surface contact, and Jump does not. Neither does anything in the GMR. Technically, neither does Cautious Move, but it’s neither Climb nor Jump, so it doesn’t meet the requirement of needing to declare Climb for vertical traversal or Jump for aerial traversal. Climbing Plus effectively deletes the Climb skill by permitting the trooper to always waive the requirement to declare Climb for vertical surfaces. So Climbing Plus permits vertical Dodge movement (or Cautious Movement) as you are not obliged to declare Climb on vertical surfaces anymore. Super-Jump only shortens Jump to a Short Skill/allows you to double-Jump as an Entire Order, but it doesn’t waive the requirement to declare Jump as your movement skill for traversing an aerial path. So the reason Dodge movement may not include aerial travel is that it’s not a Jump skill declaration so doesn’t meet the requirement that you declare Jump to declare any sort of aerial displacement path. For the same reason, even with Super-Jump you can’t declare an aerial traversal with Cautious Move. This really could all have been explicitly stated in the GMR.
A better construction would have been something like “once you have decided on a movement path, check to see what Skill you must declare to move along that path. For horizontal surface movement, you may declare Move or Cautious Move. For diagonal or vertical surfaces, you must declare Climb. For a movement path that is not in contact with a horizontal, diagonal, or vertical surface, you must declare Jump.”