Thus much let me avow— (3)
"Avow" is an important word here. The speaker wishes to make a strong declaration of fact, which suggests that he wants to be certain, rather than skeptical, about something.
You are not wrong, who deemThat my days have been a dream (4-5)
The speaker doesn't say that the woman is right, only that she is not wrong. The speaker seems unwilling to accept the skeptical position that life is all a big dream. There's a wee bit of hesitation there.
All that we see or seemIs but a dream within a dream (10-11)
The speaker sure seems pretty convinced that life is just a dream within a dream. But skepticism is supposed to be about uncertainty, so this doesn't seem so skeptical to us. Can you really be certain about uncertainty?