How to change Apple ID password used for iTunes (not iCloud)

I'm a long-time Apple user with 2 Apple IDs.  One set up for Mobile Me, which became iCloud. This account is associated with my Apple hardware purchases and Mac app purchases.  The other AppleID was set up for iTunes purchases, so that's where my purchases of music, iPhone/iPad apps and video/podcast subscriptions are recorded.  This "oops" was recognized by Apple years ago, but they made separate accounts work OK. 

Today I finally decided I should change the passwords to both Apple IDs, which I have not revised for many years.  

Changing the password to the AppleID associated with my iCloud account was tedious - cause I signed out of all devices and had to sign back in - but now all devices seem to be working with the new password.  

But, I haven’t been able to find a way to change the password to the AppleID used for music, iPhone apps and subscriptions. There is no place to change password in Music app; just Sign Out and Sign In. I logged into web at account.apple.com, but cannot change there because I’ve turned on stolen device protection.  I then tried going thru Apple’s support page.  Eventually got a web page that told me it would send a password reset request to iCloud account, which isn’t the account I need changed.  When I tried again later it gave me a choice to 1) use another of my devices, 2) use a friends Apple device, or 3) use Apple device at an Apple Store.  My concern is that any of these three options will direct me to sign into iCloud using using the AppleID associated only with iTunes purchases.  

Would the easiest path be to temporarily turn off stolen device protection on all my devices, then change the password at account.apple.com?  Otherwise, Apple seems to have associated changing AppleID passwords with logging into iCloud.  

Thanks for any assistance.  

P.S. I am aware that there is a tool to combine Apple IDs, but I’m just trying to solve one (simple ) issue today.