My 7th grade English teacher would definitely flunk your 7th grade English teacher.
Here is a simple way to determine the correct use of I or me. Take out the other person and use “I” or “me” as a stand alone.
Thus, would you say:
“I try to ...” or “Me try to ...” ?
As you can see, in this instance, “I” is correct, therefore “the speaker and I try to ...” is grammatically correct, not “the speaker and me...”.
“What youve seen the speaker and I try to do and, ...”
= = =
Nope.
‘the speaker and I’ are the object of ‘have seen’, so we need the object pronoun ‘me’ and not subject pronoun ‘I’.
Using your test: ‘What you’ve seen I try to do’ does not fly.
So my 7th grade teacher has your 7th grade teacher in a headlock.