Hey there! My husband recently transferred some existing credit from existing Chase cards to a new Chase Sapphire Reserve, so hopefully this anecdotal evidence can be helpful to you. It’s really good that you’re continually assessing your credit cards to see if they still match your needs!
My recommendation is to not cancel all three of your current cards at once. Any time you cancel a card or apply for a new one, there’s a ding to your credit score (it’s temporary, but still a ding nonetheless). And canceling a card lowers your total available credit, which can affect your credit utilization ratio and make it easier to use more of your credit each billing cycle. This can negatively affect your credit score, too.
Start by applying for the Chase Sapphire Reserve. If your application is rejected, you can call Chase and find out why. In my husband’s case, Chase determined they had already extended him enough credit through other cards, but he asked if he could shift some of his credit out of a card he didn’t use often into the Reserve, and they said yes. So, it never hurts to ask!
If you get the Reserve and still want to cancel your other cards, space apart the cancelations. You have 30 days after the annual fee is charged to cancel and get the fee credited back to your account, so consider waiting until each fee is due (assuming it’s not all at once) to cancel the cards. Keep in mind that once your Southwest and Marriott cards are no longer open, any remaining rewards points you have with both loyalty programs will expire in 2 years, so make a plan to use up what you have left if you can.
Also, if you’re less than 6-12 months away from taking out any kind of loan (mortgage, auto, etc.), be careful about applying for or canceling credit cards. Keep your credit score as high as possible so you get favorable loan terms. Hope this helps!