Welcome back to the road (for better or worse)! You've already gotten some good advice here. My own two cents:

Yes, definitely concentrate your travel on one airline program to the extent possible. After your reach top status, it's more of a judgment call that, as others have emphasized, that depends on your travel patterns and preference. I like accumulating miles on both UA and AA partly because it opens up more options for the main way that my wife and I use them, which is for business or first class international vacation travel. But if you're just flying domestically, you may not accumulate enough miles to make that an option (unless you'll be on the road as much as George Clooney in Up in the Air).

Are domestic upgrades important to you? If so, does sticking with Alaska's program get you a good chance of them when you fly partner airlines such as AA? If not, you might want to switch to AA or UA.

Congratulations on getting your points reinstated with Hilton! As for where to stay after you get your five more Hilton stays under your belt to complete the reinstatement, my basic take is that Starwood is a better program and has nicer overseas properties for cashing in your points, but Hilton has many more options for more places in the United States, plus the added perk of free breakfasts if you reach Gold or Diamond status. Which one to concentrate on will hinge on your travel budget and the places you'll go to.

Though you mention that your business expenses spending will be concentrated on the corporate Amex, it still might be worthwhile for you to get the Hilton and/or Starwood Amex cards simply for the bonus points for initial spending, which in both cases can work out to the equivalent of a free night at one of their better properties. Someone already described the Starwood bonus. If by some chance you spend $30K per year, you also get Gold status on that. Hilton now has a Hilton Honor Surpass Amex Card. (Surpass is just the fancy name HH has attached to the card.) I don't know what their current bonus offers are, but last year it was 40K points for signing up and some initial spending, plus Gold Status for the first year. Then, if you spend $20K per year you retain Gold status and for $40K per year you get Diamond.

One thing about these Amex bonuses, though: If you sign up for either or both cards, print out or do a screen save of the bonus points offer. There are separate threads about Amex reneging on such offers if the customers can't prove that they signed up for them.