You say the only thing you're really interested in is the miles, which tells me that redemption is a key variable and the cash back offers listed above aren't what you're after. Given my experience with rewards availability and ease of booking / lowest price, I would go AA vs UA or DL. DLs in particular is terrible and AAs is great.

I always take a long view on these things - I wouldn't assume you'll be able to put $360k spend on your cards forever; you'll get promoted, sell your company, or switch jobs at some point and might lose that opportunity. Also, the rest of your life is a long time, and who knows when you might need or want to travel more. Therefore, if it was me, I would do the following:

1) Get an AMEX Centurion card if you are able and don't already have one (you might need to spend 500k vs 360k though). The hotel benefits you'll use when taking the vacations you list will probably pay for themselves in short order, and once you're a Centurion member, you're always a Centurion member, so once you aren't in a position to spend $360k/yr anymore you'll be happy you got the card

2) Go AA. Do an AA Platinum challenge (which can be met with 1 round trip to Europe over a weekend for < $1,000) to get status (which removes the 100,000 miles / year limit on the credit cards) and get their Citi AA card(s). You'll get 360k + up to 150k bonus miles the first year, with the soft landing policy you'll drop to Gold status the next year (which still removes the 100k cap) and get another 360k the next year. Assuming you manage your program the right way (buying a few miles or signing up for a few offers, or just travelling for business) you can hit 1,000,000 total program miles and get Gold for life, which removes the cap permanently. Then you can continue to accumulate 360k miles forever and redeem them on the easiest program out there (IMHO). If you spend 360k for another 3 years then you'll be lifetime plat; and the only plane you every paid for will be the Platinum challenge one.

OR

2) Go DL. I personally don't think this is the best option, but you can hand out 6 Delta reserve cards, each of which earns 60k miles and 30k MQMs for each $60k spent, and the MQMs can be gifted to you by the cardholder. Thus in a given year you can get 360k miles and 180k MQMs (enough for their top level Diamond status without ever flying). As compared to AA you get better status (though getting lifetime status will take twice as long). However, you will have to pay a lot more miles on average to book your free flights vs AA.

If you care not at all about status (which you seem to say, but I find odd - nobody always flies business class for the rest of their lives) then I would agree with the other poster and get the SPG card. No status, but you get 1.25 miles per $, so you'll be at a half-million miles per year or so.

However, based on the vacation travel you list, 360k / year should be enough to get you where you want to go for free - I'd still go for one of the lifetime status approaches.