Hello Dan,
Playing with URl structure is considered as a risky business. It’s highly rewarding or disappointing. I personally do not want to change URL structure but as you said, No recent hits & ranking so its worth a try as there is nothing to lose.
There are many things to consider before you implement the changes which cannot be explained here (you can read on internet, which we SEO mostly do). As far as your questions are concerned:
**What do I need to keep in mind when deleting posts, categories, and tags - besides 410, Google URL removal? **
When you make a link 404,410 make sure, every internal anchor (pointed to 404) should be replaced with suitable link or removed. There should be no reference of 404 link on website including sitemap, old navigation or images.
**What do I do with all the old posts that I am going to re-direct? Each post has between 10-15 internal links. I've started manually removing each link in old posts before 301'ing them. **
There is no need to replace the internal links of article which need to be redirected as they will be null and void (uncrawlable/ inaccessible) after redirection. But make sure every instance of internal link pointed to old url should point to new redirected Url (to keep things less messy and quick).
Best of luck