Not at all.
I'm wondering why you expect the websites you're attempting to utilize to understand your intentions are "pure" when I would argue that setup is vastly more commonly used for nefarious purposes.
They do blocking for a reason. I'm sure if you contacted them they would explain they lose $$$$$$ a year due to fraud/abuse/hack/nefarious attempts coming from setups similar to yours, which dwarfs however much you might buy from them. I understand their position.
There are commercial VPN and security solutions etc that would achieve some of the goals - undoubtedly at a higher cost than what you're running. You would essentially paying for a boost in reputation that websites would recognize as being more on the "good" side than "bad".
It's quite unfortunate for you I agree but I don't blame them at all.
A suggestion - get a more premiere data center host and get a /29 network allocated to you (can be using a LLC for privacy). Essentially become a commercial entity and pass the sniff test for a lot of websites.
Or subscribe to a service that does that for you, and your frustrations will melt away.