Most migration plugins should work with Local, but we don’t have a list or instructions for each one. If you search the Local forums here, you should be able to find posts and threads for many of the plugins in your list to see if something is worth trying. We generally recommend WP Migrate, which, in transparency, is part of our family but was already one of the most popular before falling under the WP Engine umbrella of products.
For just a general push to a host, they have a walkthrough here:
They have some other documentation on their site below as well, and they also have product support teams if you have any specific questions about their tooling. They may have limited availability however until after the new year.