Nice job perks, and you're smart to maximize them in a longer term way.

As you and others have noted, your main critera is that you accumulate flexible and stable rewards, but also diversify.

Based on where you said you're usually travelling, you'll build up status-earning miles quite quickly on AA. Focus on that for your butt-in-seat earnings. Once you attain a higher level status, you should start earning miles with a bonus tacked on. In short, you should consider your AA needs met through your physical travel. You can perhaps leverage the AA status as a challenge on another airline in the future.

In terms of purchasing things, about the most flexible and valuable points you can get are Chase URs. I'd get the Sapphire Preferred and use that for your airfare and rental cars, dining etc.
Also, book your tickets, hotels, car, etc through the UR portal, and you get extra pt/$ for travel related purchases.
Your employer is quite "nice" that they do it last minute, so you get tons of points for a single ticket purchase. ;-)

Then, also get a Chase Marriot Premier card. Use this whenever you stay at a Marriot (and purposely book there, in the cities where you can) to earn 5x Marriot pts. Those will build up fast, and there are Marriots everywhere for your future redemption.
If you can't / don't want to stay in a Marriot then use the Sapphire. UR > high-end Hyatt is a very lucrative redemption.