{na ku ko'a ja'a cai bajra} means "It is not the case that he
is very much running (but he might nonetheless be running to some
other (lesser? -- details yet to be thrashed out) extent", IMO.
That is, the information added by {cai} falls within the scope
of the negation.
This is probably not relevant to you point (with which I agree), but anyway... Shouldn't {ja'a}, given that it is in NA, have the same exporting privileges as {na}? In that case, you'd have to say {na ku ja'a cai ku ko'a bajra} to get the wanted scope.