I noticed sentence "Powered by mempool.space and Coindesk." on your website. Have you checked whether those free API actually let user check thousand address within short time?
No, you can't use thousands at once. It won't load. You need to make a few each time.
That's what i expect. Which means it's not suitable for those who wants to check lots of address quickly.
You can also check the BitAC Android app. It's an open-source android app, and the codes can be found on Github. I haven't tried the app yet since I never had to check multiple address balances at once. You may want to try it and let us know if it works 
FYI, that app utilize blockchain.com API[1-2], which already suggested by other member.
[1] https://github.com/ademar111190/BitAC/blob/ebe3dc69e21ad744c6689fb4ef6db5adf85bc169/Android/app/build.gradle#L26
[2] https://github.com/ademar111190/BitAC/blob/1c3b508b8bedbe140afd05e810490b0bc5e4e2cf/Android/app/src/main/res/values/strings.xml#L56