An example textbook sentence:
かかるついでに、見たてまつり給はむや How about looking at him (Genji) on this occasion?
たてまつる is humble auxiliary, 給ふ（給う） is honorific. Does this reflect a relationship between 3 people, where:
speaker - 給ふ - addressee - たてまつる - Genji
So speaker is both elevating addressee's status with 給ふ honorific while also humbling him before Genji?
Your great, concise description agrees with the following Q&A :
http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1132656341
（僧都が尼君に）「この世にののしり給ふ光源氏、かかるついでに見たてまつり給はむや」 （源氏物語）
ののしる today means "to curse, badmouth, ..." but in Genji's time it meant "to be famous" among other meanings.
This Q&A page also explains the penultimate 「む」
「む」には(1)推量・予想、(2)意志・決意、(3)適当・勧誘、(4)仮定、(5)婉曲という五つの意味がありますが
In this text, it is (3)適当・勧誘 == 適当…［～がよい］, 勧誘…［～しませんか］
( One minor point: the addressee 尼君 is female, so the speaker is both elevating addressee's status with the 給ふ honorific, while also humbling [her] before Genji. )
見たてまつり reminded me of "A cat may look at a king."
