i have similar questions about what might be the best strategy to do what you want.
for myself, i have needed to make iCloud separate accounts in 3 app stores (Japan, Hong Kong, and USA) in order to be able to download and maintain apps and content.
the other day i needed to access the hong kong iOS app store to download the Hong Kong version of the HSBC business app (which is only available through the HKG app store).
the only way i know how to do that is to sign out of the iTunes & App store on my iPhone temporarily, download the HKG app store app, and then sign back into the iTunes & App Store in my home country (Japan).
the good news is that the HKG app, and the apps that were/are only available in the USA store, once they are on your iOS device, they can happily stay there and co-exist with apps/content that were downloaded from other app stores, and are even updated normally, even though you are not signed into the store from which you originally downloaded from.
many years ago i bought and download TV content from the USA iTunes store.
i downloaded that content (purchased in USA iTunes TV store) to an off-line device (that could be accessed and loaded into iTunes at any time, but just not located in the main, current apple Music library.
i havent signed into the USA store in over 2 years, the content, but still can access and play that TV content that is being stored outside of the Music main library. so it must check for where it comes from originally, but doesnt care if it is associated with the current iCloud ID you are singed into Music/iTunes with.
but, signing out of one app store will delete the apple Music content that is already downloaded to that one device's Music library.
so every time i sign out of the Japan iTunes & App store, it deletes all the downloaded music that was on that one device in the main library associated with that ID.
when i sign back into that account however, the music titles and playlists are all there in iCloud, but it takes about 1 or 2 hours to get it all downloaded back to that device (i fly a lot and want access to music and content all the time).
i have also found that you do not need to have a credit card in every app store. this has changed over the past 4 or 5 years. there are ways to set up the app store ID to be used for only free apps/content. and doing this has become easier and easier.
your idea of using iTunes Gift cards does work.
however, you mention you have iTunes Match.
the horror stories about iTunes Match not working across different iTunes stores (let along within the same) stores are legion.
it is for sure that downloaded Music content will be deleted as above if you sign out of yr current ID.
getting iTunes Matched songs and albums back onto yr device is likely to have problems.
(i dont have iTunes Match, but the net is full of bad episodes since allowable versions and special versions of songs available for download and purchase varies so much due to the digital Rights in each country having no consistency).
however, in my case (not iTunes matched music): music that i had purchased long long ago before iTunes became apple Music, however, do have a life of their own. apple consistently does recognize that i actually did purchase it at one point, so that music is not deleted.
apple does have a consistent way of leaving that music on my device when i switch stores.
i dont know if iTunes Matched content works the same way or not.