The safest path seems to be:
For each category (personal, business):
First lower the credit limit as much as possible.
Then wait a month or more. (Ie, lower the credit limit soon after you get the card; don't wait until you're ready to cancel!)
Only then close the card.
Only then apply for a new card.
Reasons:
1. Closing a card locks up the credit limit on that card for another year or so!
The only way around that is to lower credit limit first, but that also takes a while (though a much shorter while) to be reflected in future card apps.
2. Some people are getting denied these days if they are applying for the same kind of card they already have open.
Finally, be aware that if you are not given at least $5k of credit limit on a personal card application, you will have wasted that application, because you'll be issued a Plat card with only a 5k bonus, instead of the Signature card with the 30k bonus!
This issue doesn't exist with the Alaska business cards, there you either get approved and get 30k bonus, or you get denied, it's much simpler.