Question about dual possesive nouns [duplicate]

I am writing a technical letter for my (and my lab partner’s) senior design project (we are engineering majors) and I would like some help on properly phrasing part of the letter.

The project belongs to my partner and I. I was always taught in school that in cases of dual possession, I should always proceed the other possessors.

Suppose for a moment that the project was just mine. Then in that case, the sentence below would be grammatically correct.

Attached to this email is my project selection.

Now if the project only belonged to my partner, this sentence would also be grammatically correct.

Attached to this email is my partner's project selection.

However, since this project belongs to both of us, I need to phrase the sentence accordingly.

The sentence below doesn’t appear to be correct in my opinion.

Attached to this email is my partner and I's project selection.

This one sounds better, but doesn’t follow the rules I was taught.

Attached to this email is mine and my partner’s project selection.

So which phrase (if any) should I use to be grammatically correct? Thanks

Whenever you want to write "he/him and me/I", reverse the two pronouns and see if it sounds right.

Also, omit the "he/him" and see what that sounds like.

Your sentence would read "The project belongs to I and my partner" (obviously wrong), or "The project belongs to I" (obviously wrong).

Another idea: Write out both cases:

"Attached to this email is mine and my partner's project selection" becomes

"Attached to this email is mine project selection." and

"Attached to this email is my partner's project selection".

Can you see what's wrong?