You've identified the fundamental problem, which is a good thing. Likewise, you have recognized that any form of inline scripting contradicts the working principle of a page cache. Actually, the requirement would be predestined for ESI, but ESI also has significant disadvantages that can be so...
To avoid misunderstandings, the LiteSpeed web server and LScache basically have almost everything ready to meet even exotic requirements. In principle, a plugin could also meet these requirements. But a plugin is just a plugin and therefore has a fixed range of functions, because you can only...
Instead of inspectlet use Matomo and host it on your own server. Matomo is as good as Google Analytics. Host all fonts on your own server and not at Google.
Yes and a dedicated server wouldn't make it faster, because your problem is not the server. Most of all requests come from external hosts like Google, Facebook and so on. Kick them off and your shop goes 3-times faster, atleast!!!
For developing I have the same. On this server I have around 10 different shops running. The biggest one is a Shopware shop, similar to Magento and this Shop has around 50,000 products. It is fast, really fast, so I think you don't need a VPS.
I think you are a dreamer? ;)
There is no provider in this universe who allows a higher max_execution_timeout higher than 300s on shared hosting. The same with memory limit! If so nobody would pay for a dedicated server!