I too am thinking we're missing something in this conversation, but not yet sure what.
The way we expect an upgrade from 5.6.9 to 6.2.4 to happen is
- upgrade all client applications not to use any features that were deprecated in 5.6.9.
- upgrade Elasticsearch via a rolling upgrade.
These steps do not need to happen simultaneously: by design, it should be possible to modify client applications to be compatible with 6.2.4 while they are still running against 5.6.9.
If your application is trying to create new indices with multiple types then this is a feature that was deprecated in 5.x, and you need to upgrade the application to only create single-type indices before upgrading Elasticsearch. You can do this while still running on 5.x, because of course 5.x supports single-type indices too as a special case of multiple-type indices. Once the application is so upgraded, any existing indices will remain as they are through the upgrade, and you can still index into them and search them, without needing to reindex them into the 6.x format.
It's wise to fully rehearse this upgrade in your test environment before performing it in production. This means starting with the same versions of your application and Elasticsearch as you have in production, and running through the upgrade procedure, verifying that everything still works afterwards. If it doesn't, the best thing to do is to reset the test environment to match production and try again with a new procedure. You mentioned using Homebrew to upgrade one of your environments. If this is not how you will upgrade your production environment then it's not a good test of your upgrade procedure.
We're unlikely ever to be able to say "yes, this upgrade definitely won't break your production environment" because there are far too many variables outside of our control. We may be able to offer help with your upgrade procedure if you cannot find a way to do the upgrade without reindexing, but this may require some iteration: in particular, you'll need to be able to reset your test environment to match production and try the upgrade again.