Another I or Me Question

Okay, let's remove John from the conversation. Thank you for meeting with ___. What word goes in the blank?

(Don't capitalize "Me.)

You know someone told me about that rule - but I'm not buying it - no disrespect intended. I think "John and me" sounds terrible, but maybe that's because I am from Ireland originally and the American convention is different.

Well, I certainly invite you to get the opinions of speakers from the British Isles on whether "meeting with I" is appropriate.

Too many people grew up being chastised for saying "John and me went to the store" and now fear any such combination, even when it's the object. Do as you wish. No disrepsect intended.

You wouldn't say 'Thank you for meeting with I'. It's definitely 'me'.