Very interesting topic and while I fear, I may not be a direct help, as there are a lot of things which may be better served from a hosting perspective or otherwise fall outside our scope of support, I hope clarifies some of what you asked. (Of course invite others to chime in.)
The biggest impact of the "score" that I see a lot are actually from third party services/resources being integrated. This includes all around from your server, to within our software, to even Javascript you load into the software. Even using Google's own PageSpeed tool, it will flag and bring down your score for using AdSense and some more of it's own products (which I always thought to be ironic). Everything will need to be weighed on whether or not you need the integration and what impact it brings to your goals.
There are some items like "Remove unused CSS or Javascript", "Eliminate render blocking resources", etc... basically, anything that requires editing our core code will not be something which we support so these items would be up to us under our support policy to help improve.
While, I do not believe this may have been the answer you were looking for, I hope it helps.