MarsEdit 4.4 now supports Micro.blog and can search the values of custom fields. However, there seems to be a regression that causes the app to beachball for 30 seconds each time I publish a post.
Update (2020-08-03): The performance regression is fixed in MarsEdit 4.4.2.
In January, 2020, Google stopped allowing MarsEdit customers to authenticate with the [Blogger] service, because MarsEdit is not a “verified” app. The guidelines for making MarsEdit comply with Google’s requirements are rigorous, and there is no guarantee that MarsEdit would continue to be supported for the long term. We decided to to end support for the service rather than invest any more effort into what would be, at best, a lackluster user experience with the lack of photo-uploading support.