To insist that "(bridi)" express the same proposition when bare and when in "operator (bridi)" is to insist that the syntax/logical form of bridi must be determined solely by their morphophonological structure and not rules, such as scope-leaping, that allow (carefully regulated) mismatches. Such an insistence fosters simplicity of rules, but is not very utilitarian. Lojban already has mismatches for sure, e.g. "(na ku zo'u) ma broda".
Take the present case as an example. Suppose you want to say "zo'e ge broda gi poi'i mi jinvi lo du'u ke'a brodu". By the candidate rules I'm counterposing to yours, that could simply be rendered as the morphophonologically simpler "mi jinvi lo du'u lo broda cu brodu".
When it is used to refer to the asking of a question, it is an
argument of "... is the reason for ...", but when used to ask a
question, it is not. It just happens that we can conveniently use it
for both things at the same time.
In "use it for both things at the same time", what is "it"?
As I understand it, I'm saying that the logical form for the sentence contains only the illocution "I hereby ask whether", while you are saying it contains both the illocution and a separate referential description of the illocution. But in that case, there is nothing that is being used for both things at the same time.