Welcome to flying. I guess we all have had some horror stories that we lived. Most of the time these are related to weather, mehcanical difficulity, and our preception of what should be done for us.
I am glad you checked some of the rules before writing. It was also good to run it by some of the people here on the site. I will provide you some other insight that you will might want to consider when you write.
On the trip out "AA unilaterally change the plane flight time". You will see that they retain the right to do just that. Who would they have to ask, anyway? Secondly, you will find on the ticket/or ticket jacket a notice to check your flight the day before take off to insure your itinery has not change. It is also important to leave a "notice" phone number, so they can notifly you of changes (some times it does happen, I have been so notified). So you may be partly a party to your own trouble on the outbound flight. That is not to say you can't try to get something out of AA for your inconvenience.
On the way back, you got caught in a mechanical, then weather related delay. Both, according to the rules are "not the airlines fault" (one could argue that better maintenance would drastically reduce such delays). The offer of a free room or 1/2 price room is a matter of contention. I am not sure on this one. But you chose not to take either but to Unilaterally decide to rent a luxury car and drive home. That is the other way of looking at it. So make sure you deal with those thoughts in mind when writing. Needed to be home. Car reimbursement would be offset for them by your not taking a room and your not taking the rest of your flight. That approach may work better. Inconvenience compensation is rarely more that more discount vouchers, or a marketing tool to get you to fly them again.
Don't be surprised if you have to rewrite and remind. As far as writing the President or the BOD, why waste your money. These letters are not read by anyone near those levels, but referred down the road to oblivian.
No one win. AA certainly does not benefit. You certainly did not benefit. It already cost AA money for hotels, transportation, meals, etc. You are out for a car and a very miserable time.
You have a chance to improve your position some. Take it calmly, and look at both sides, then request something reasonable, or at least make sure it appears reasonable.
Those are my thoughts anyway.