I'm curious: Why do you want to get ideas first from people who have not seen/heard you play, rather than from your teacher?
In general, be more fluent, musically.
Your teacher would have a better idea of what's hampering your fluency than we would.
I know some theory, and have a good ear, but feel restricted.
We don't know what theory knowledge you possess, nor what you mean by saying "I...have a good ear, but feel restricted."
I realize that these are long term goals and would like to re-structure my lessons to reflect them better, because I will only make progress in something if the lesson somehow covers it. And I do wish to continue learning pieces, just not 100% of the time.
This is something you should run by your teacher. We can't help you with restructuring your present lesson format to something else with such limited knowledge of your strengths and weaknesses. (And no amount of writing about them will substitute for actually seeing you playing.)
My question is what would you do during a lesson in order to strengthen these areas?
There's no single answer to strengthening the areas you mention. Teachers tailor their instruction to their students' unique strengths/weaknesses/needs.
How would you organize/divide the lesson to make a direct, measurable progress in these areas?
I organize my time during lessons according to each student's individual needs. Music theory, for example, might be 1/6 of the lesson time, or 1/3 of the time, or something in between or outside of those bounds. It depends, too, on how long the student's weekly lesson lasts. A 30-minute lesson might get only 1/10 of the time for theory (3 minutes). Students taking 45- or 60-minute lessons might get, say, 10 or 20 minutes, respectively, for theory. Depends on goals, time available, and other factors.
Some weeks the time structuring may vary, too, even for the same student. More emphasis on repertoire one week; theory another; technique yet another. A flexible teacher, while having a general lesson structure in mind, will also be thinking on his/her feet, adjusting as needed in real time, according to how the lesson unfolds.
I second Peter's recommendation that doing two one-hour sessions a week would much better help you reach your goals.
I have a teacher who is very flexible and open to requests, I just want to get some ideas from you first.
I would recommend you start by telling your teacher what you wrote in this post. Ask her/him what s/he believes will help you achieve these goals.
Best wishes to you.