Office 2016 does not work with MathType: Migration of Word documents with MathType equations
I just received this note from Mathtype, much more reassuring than I was expecting. In the meantime, I might try doing my word+mathtype work in Parallels.

Actually some versions of Office 2011 do work on High Sierra, but not if you continue to update to the latest version of Office 2011. Naturally updates are important for security reasons, so we don't recommend our customers stay with an early version of Office 2011 forever (I'm using 14.7.2, and it works fine).

It shouldn't be long though. We're hard at work on MathType 6.8 (which we think the version number will be) for Mac. We've been working together with Microsoft on this, and we have early betas now that we're using and testing within the company. It does integrate into Word 2016, with a MathType tab and commands on the tab similar to those on Word for Windows. We do have some things to work on, but our progress so far has been encouraging -- over the last couple of months anyway.

You may have read about our merger with Maths for More, the company behind the WIRIS equation editor (http://news.dessci.com/mathtype-and-wiris-join-forces). One result of the merger is that you will soon see more frequent releases of MathType (monthly is our goal), but our highest priority right now is releasing a version of MathType for Office 2016 on the Mac. The company isn't projecting a release date other than "in coming months". I'll be more specific than that and say I estimate it will be 8-12 more weeks. We're maintaining a list of customers who have asked about it, and those on the list will be among the first to know when we have news to report.