That lacklustre support response was enough to put me off the service. And then, funnily enough, a few days ago I received a reply from Sendgrid support about another account I had opened for a side project. This reply came in ~2 months late, where I was asking if I could be moved to a different IP range as all my emails were getting blocked by Outlook services due to the shared IP I was assigned being (seemingly) misused by spammers. Again, the response was "just keep trying as normal" and eventually my emails would work... Apparently. That's obviously not a viable business communications strategy.
The funniest part about both these support responses was that despite one of them taking several weeks to get a response, I'm being pinged every few days asking me if my issue was solved. It's all well and good for me to wait months when I need a response as to why all my emails are getting sent to spam, but as soon as the ball is in their court, they don't mind pestering me for a response.
I don't have enough bandwidth for a dedicated IP, so I signed up for a service that requires a credit card even for its free plan, which I believe is a decent enough barrier against spamming.