I think i can see a way of having progressive speed and jump without having any attributes or skills related to those actions. Race will determine who starts where and after that your characters abilities are determined by overall level increasing each level based on a race specific multiplier with different ceilings for different races. See we don't need attributes anymore.
Ummm... the numbers you're talking about - the "who starts where" and "abilities... determined by overall level" ARE attributes. Exactly what you've done is to propose attributes of speed and jump height. Not calling them that doesn't alter the fact that that's what they are.
Speed and jump height should be determined by a combination of factors - including but possibly not limited to race, height, weight, encumbrance and the amount of time one has spent running and jumping. Increases should be entirely in the background - as your character runs more, s/he gets faster. As s/he jumps more, s/he comes to be able to jump higher and further. Those abilities should start at a particular point, governed by race, height and weight, and should have caps also determined by race, height and weight. And they should always (and I mean
always, no matter what your skill level might be) be modified by encumbrance. Stamina shouldn't enter into it at all, really - that doesn't determine how fast you can run or how far you can jump, but how long you can continue running or continue jumping.
I don't expect that it'll be even vaguely like that though.....