For swapping the numbers - yes that is possible, although you may irritate AA gate agents by doing it.

For CX remember that:
- the qualification year is 12 months from whenever you join or last changed status
- when you go up a level your Club (status) Points & Miles get reset to zero, so you need 210,000 miles to get to Diamond from nothing
- if you don't keep status up you can drop all the way back immediately, not just one tier per year.
- no status bonuses
- the benefits on CX as a Diamond are good (guaranteed seat at cheapest published fare in Y; guaranteed seat in full-J, lots of upgrades - although generally only if the booked class is full, lots of recognition).

So it's hard to get, quite an exclusive club, and IMO worth it if you fly CX a lot. But you have to fly a huge amount to keep EXP and get to Diamond in less than 2 or 3 years.

Personally I use them the other way round - CX Diamond as my primary status, and then putting whatever is left over into AA, this being enough at the moment to be either Plat or EXP most years. AA has the advantage of lifetime status, which CX no longer has, so there is no real reason to keep putting flights on CX once Diamond requalification is achieved.