Right now if you copy and paste an actual Unicode emoji [url=https://emojipedia.org/thinking-face](e.g.)[/url] into your post, and try to submit it, the forum returns some error about an invalid string.

I believe this is a collation issue. The MFGG forums run on a database that stores all kinds of information about your posts, user accounts, and so forth. This database is coded in a way that doesn't support extended characters. I could use a test environment to see if changing the character set is possible (and wouldn't cause performance issues or break anything). However, I'm now more focused on adding features to the new forum system we're developing, rather than supporting nice but nonessential features in phpBB 3.0.12. In the meantime, you could always use one of the built-in emoji/emoticons, or you could display the emoji as a regular image.