Flying with a larger cat

Greetings! I'm a graduate student with a 17.5lb Maine Coon. I anticipate some airline travel in a couple months and was wondering if it's a lost cause to try to get the cat into a medium sized pet carrier and into the cabin... American Airlines has a 20lb combined weight of pet + carrier, and a Sherpa (for example) medium sized American Airlines or similar is around 3.5 lb, maybe 4, so total will be 21.5 or so lb. Are they sticklers for total weight? I'm sure the cat can fit in the carrier and the flight is not a long one. American is the only airline that serves my college town.

So, what's the best way? it is expensive to fly to begin with, and they want $100 or so each way. Will they be strict on total weight? can one use the medium or large Sherpa carriers and a larger cat? is it worth doing a dry run with the carrier to the airport and asking? it's not a busy airport (3-4 flights a day) so I'm sure they'll take their time

I'm going to be traveling for two weeks so boarding at $15/day is about the cost of the cat ticket... I'd rather not leave the cat for that long. He's very people oriented and needs people so a pet sitter in my apartment will not work.

Any thoughts? Are other airlines more 'lenient' in terms of weight? I could swing it by taking a shuttle to a larger city and flying Southwest which does not mention cat weight

I've never had to do anything like that so I don't have any personal experience to share.  Here's an article that, if you scroll towards the bottom of the page, gives information for some of the different airlines.  http://www.moneycrashers.com/traveling-with-pets-airlines/

Welcome to TCS!   I hope you are able to figure out the best way to travel safely with your kitty.   

Southwest allows cats and dogs, $95.00 each way. Carriers must fit under the seat. Details on SW.

For airplane travel, using the fabric carriers is usually the best option.  It fits under the seat much better than a plastic carrier if you have a large cat.  I would definitely do some dry runs with him and the carrier, like putting it on the floor of your car and getting him used to napping in it.  I have not flown with cats for a very long time and the rules may have changed, but I do think the important part of cabin travel (and I would NEVER put them in baggage) is that the carrier fits under the seat in front of you.