You shouldn't need an updated plan to handle this. It seems as though every page load is hitting a database. I can't see the page since it won't load, but I'd imagine the content here can be easily cached.

If you don't want to pay more or deal with technical details like setting up cache servers, just put it behind CloudFlare or similar temporarily.

This is the best answer. Cloudflare free tier CDN is amazing, and is ridiculously easy to set up. They even provide and set up an SSL certificate for you.

Reduce the max users in your http servers. Your max database users should always be a bit less than your max http servers/instances/connections.

Http will queue connections if over the limit and everything will just work without errors. You won't even have an overloaded server (although some users may have a long wait).

If your database can’t handle the load, your queue will grow indefinitely. So users will have an infinite wait or timeout. Not a panacea.