As a short term solution, have you considered Cloudflare? If Google is repeatedly crawling the same static pages, you can have them served from the Cloudflare cache instead, and the free version should still have the features you need.
Another option would be to move to a dedicated server. You can get quite a powerful server from a company like LiquidWeb for a few hundred dollars a month. (A "managed" server, so although a bit of know-how is needed to get it performing optimally, they can help you with the basics at least.) I expect with a bit of tuning of your web server (nginx or even apache with mpm_event or worker) you could handle that level of traffic even without caching, but you could also use something like Varnish to do even better.
Another option would be to move to a dedicated server. You can get quite a powerful server from a company like LiquidWeb for a few hundred dollars a month. (A "managed" server, so although a bit of know-how is needed to get it performing optimally, they can help you with the basics at least.) I expect with a bit of tuning of your web server (nginx or even apache with mpm_event or worker) you could handle that level of traffic even without caching, but you could also use something like Varnish to do even better.