J.R.
I have not flown with that seat, but I have been on SW many times (including this past week) wiht a britax marathon and a go go babyz wheel attachment (which is AWESOME!)...I have found that it is best to use a seat belt extender (although this is mostly because of the wheels)...my best advise is that one of you should go on first and get your seats and put the car seat in...Stay calm while doing it! I make the extender about half tight, then clip it into the buckle by the window side of the window seat...thread it through the back of the car seat and buckle on the other side. We had an issue once when we didn't use the extender - when tightened, the seat belt buckle ended up in the middle of the back of the car seat, and we couldn't reach it to unbuckle...
As for southwest, they are amazing! Great with kids (plenty of snacks and lids on drink cups), and they have coloring book that you can ask for...they let families board after the "A" group - which is 60 people. You can get a number in the A group if you go online to check in EXACTLY 24 hours in advance (although don't stress about this because like I said, families go between the A and B groupings). they will let your 2 year old say hi to the pilots...great customer service!