Here’s the strategy I use:
Copy the blogs from the old site to the new site without any changes. Don’t do any updates or announcement/greetings to the new site. Users must feel they are still connected to you. Since you are self hosting the old site there is no urgency to take it down. Contrary, we’re going to use it to your advantage.
Go to each old blog post, or just the one’s generating 80% of your traffic and delete most of each blog, leaving the title and first two sentences. After the last sentence of each, write a statement saying “click here for more”. Create an external link to the full blog post on your Sparkling new site.
Go into Google Search Console and register both sites as you being the owner, if you haven’t already done so. This tells Google that both sites are the owner of the content so the new site won’t be viewed by Google as a content pirate.
Keep the old site active for a few months and monitor your search traffic in Google Search Console. Once you see your traffic rising on the copied blog posts, and you see traffic coming into the new site without coming from the old site, you can delete the old site.
You’re self hosting, so unless you really no what you are doing, one mistake in a redirect could cause all kinds of problems. Redirects when done correctly are beneficial to the overall site. Content is different. You want to make sure the content, and thus user experience, flow frictionless from the old site to the Sparkling new site.