Wow. Now that's what I call a trip report! Sorry to hear that your run went so badly. It's tough to excuse all the things that happened, but in my experience with air travel, when it rains it pours. Seems like it's never just one little thing, more like a dozen little things in succession!
Having said that, I'll just make a few comments. First, I agree that AA doesn't always handle these weather situations the best. Even when they have good notice that the system is about to get fouled up bigtime, they often seem more bound by rules than by common sense. Example, last year when a hurricane blew up the East Coast and approached NYC, I attempted to move my flight up from the morning the storm was expected to arrive to the previous evening. Lots of availability on outbound flights, but even as an EXP I was refused my request unless I was willing to pay full fare. The next day, you can guess what happened - I ended up stuck at LGA with hundreds of other pax for hours as the storm came through. Only after some very strong (but polite!) words about my situation to a supervisor in the AC did I get a seat on the last flight out and a $500 travel voucher. Why cause yourself the grief, AA? Do the right thing when you have the chance and save everyone some trouble.
On the other hand, though, I've been treated well far more than I haven't; we probably all agree that AA has some really amazing employees and sometimes you just have to take a few minutes to find the right one. But in your situation at the gate, even the best reps and flight managers would have their patience tested - remember that they're the ones who have to clean up the mess, and it's not likely they're the ones who made it in the first place. I've learned the hard way that sometimes it's just better to grin and bear it than suffer the stress of fighting the unwinnable battle.
Secondly (and I really hope I don't offend you or anyone else by saying this), I know from watching this firsthand on many, many occasions that airport staff quickly become irritated by elite members constantly reminding them of their status. They're very aware of it without you telling them, and your reminders won't generally help the situation any. Keep in mind that someone who travels ORD-LHR just 3 times a year, or JFK-SFO 5 times a year, is a GLD member. (How many of us can remember the first time we made Gold and thought it was the greatest thing since sliced bread? :-) I still get a chuckle watching a crowd of Golds waving their cards at the gate agent for a transcon flight, thinking they'll surely get an upgrade this time!) It's not my intention to disparage the Gold population, but I think it's safe to say that there's just too many of them to expect a really big leap in service. Looking back on those days myself, I remember not noticing truly better personal service from AA until I became PLT, and even then the difference was minor compared to the treatment we're afforded as EXPs.
I absolutely believe, though, that there's a big difference in making exceptions vs. not providing published benefits. Elite pre-boarding is a valuable benefit that most of us really cherish, but some gate agents seem to think it's simply an option for them to offer it or not. And, of course, it makes complete sense in a situation such as yours to pay special attention to elite flyers. Anyone in any kind of business knows that if you've got to inconvenience someone, let your best customers take the least amount of pain. I think that often gets forgotten in the heat of the moment.
Anyway, really sorry you didn't enjoy your trip more. Hopefully the troubles you encountered will be soon forgotten as you enjoy your new PLT status!