"I have medications and electronics in there that cannot be checked. It will be faster for me to find a spot than to separate out those items. If you insist I will go ahead and repack the bag here. Or we can call the gate agent and see if they want to book me on a later flight."

Usually I say I am a (exp or Ck), and sorry for the late boarding but it was due to a misconnect.... and politely ask if there is some possible way to squeeze it anywhere.

The "medications/electronics" excuse is almost bulletproof as an 'issue'- their announcements specifically tell you to remove those, they cannot force you to give up that option.

IMO of course