How do I figure out what the implied subject is?

Question

I was doing some JLPT N2 practice and I came across this:

あのう、山本先生でいらっしゃいますか。私、先日、先生の講演会で（　）鈴木と申します。

１　ご覧になった

２　お会いになった

３　お目にかかった

４　お伺いした

My thinking:

Some form of 会った should be filled in the blank. So 1 and 4 are wrong. All of the options don't have a subject. So I don't know whether it is:

先生の講演会で先生が会った鈴木

the Suzuki that you met at your talk

or

先生の講演会で先生と会った鈴木

the Suzuki that met you at your talk

Therefore I am not sure between 2 and 3. And apparently the correct answer is 3.

How do I know the subject?

Answer 1

1. ご覧になる is an honorific form of 見る ("to take a look", "to watch").
2. お会いになる is an honorific version of 会う ("to meet").
3. お目にかかる is a humble version of 会う ("to meet").
4. お伺いする is a humble version of 伺う ("to visit").

Options 1 and 4 are semantically wrong verb choices. Although は is omitted, the topic of the sentence in question is clearly 私. By starting a sentence like this with 私, the listener would expect you are talking about 私, and expect a humble expression. And the blank is followed by another humble expression 申す. Therefore the subject of the masked verb is 私, and the correct answer is 3.

(In addition, 先生が私にお会いになる and 先生がお会いになった私 themselves sound a little strange to me although they do not violate the basic rules of keigo. I don't know why, but if two people met each other and one of them is 私, I strongly feel a humble expression with 私 as the subject is the default choice.)