No.
> I've been debating with myself whether I need to move my content somewhere like wordpress.com to avoid that requirement.
The biggest issue would be your log files, I've covered that in comments here, and in the articles as well. Another issue could be if you run analytics tags or advertising, which may impact you in a negative way financially in the case of advertising. My own blog is analytics and advertising free, I don't see it as a source of income so I don't care but obviously that will not hold for everybody.
The critical part is when you start to ask users to enter data into your system, as long as you don't do that you will be able to solve this in a straightforward way.
> The personal information I process comes from comments and web server logs, and I'm not sure that counts as occasional.
You are right that it isn't occasional. So, logs: analyze them, then delete them within 30 days or so. That should be enough to do most security related work with the logs as well as any analysis you care for.
Comments on your blog you will simply have to delete when the commenter asks for it. Even when I ran reocities.com this was the most requested support item, and it is pretty easy to do in an automatic fashion if you still have the original relationship between an account and the comments, this could be entirely self-service. I expect the typical blog engine plug ins to become GDPR compliant in the near future because lots of people will be asking for this.
> Or do blog comments count as a service?
Yes, it is a service. You operate a server which takes in data and records it. That it isn't commercial is not important in this case, data subjects will create accounts and there will be PII associated with those accounts, either directly or in the comments.
Now for some arguably bad advice (from a legal perspective, but it is very practical): I'd take 30 days to see how this all shakes out past may 25 before taking action on something as insignificant as a blog. That way you will have a lot more information to base your decision on. Obviously that has a risk: you will probably not be in compliance but I'm going on the assumption that regulators will have a lot more on their plate than your blog for the foreseeable future.