In my 10+ years in management, I have yet to see a move letter that authorized anywhere near $23K in expenses...
Looking at Bekins.Com, a move from LAS to MIA for a two bedroom with furnished living room came out between $4300 and $5200. Article 18 of the APFA contract used to allow up to 12,000 lbs per move (I assume it still does). Bekins shows a rate of $9751 for a move with that much stuff.
60 days of storage would run another couple hundred, but that's still nowhere near $23K.
AA has contracted rates with several moving companies, so the actual rate paid out would be less, not to mention that this all took place three years ago when shipping rates would have been even lower due to lower diesel fuel costs. In other words, whoever told you that the moves cost $23K is feeding you a line of something commonly found in blue water...
Sure, if people are forced into the base it will cost AA some money in moving expenses. The question is how much, and that will be driven by how many people actually move, as opposed to commute and hold out for a transfer back to where they actually want to live.
ORD has 2700 flight attendants, yet only about 1700 of them live in IL/IN/WI. LGA has 1200 flight attendants, but only 600 of them live in NY/NJ/CT/RI. JFK has 1700, but only about 800 live in NY/NJ/CT/RI. There are more NYC based FA's who live in FL than in NJ.
My guess is that you won't see a lot of people actually moving if they're forced to transfer. Sure, some will, but only those who plan on staying there for a while.