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.
Would it work to replace those by your own utxo dump from Bitcoin Core? It takes more resources than using an API, but won't have any limitations on how many addresses you can check.
Certainly this would be the best solution.
I believe my next project will to run my own node in an online server. I don't have it now. I will take a look on the costs and what else could I do with it.