While I'm waiting on this... Can you tell me which plugin you are referring to with "The problem is that you haven't changed the setting for the plugin." Is that by nature of what is going on? Or is that another step I am missing?
OK, I was able to discuss further with the relevant developer.
Right now, using image fields with custom sizes cannot work with the WP Media Offload plugin if a copy of the files is not kept locally on the server (that setting I was referring to).
He thought it would be a reasonable request to consider adding a compatibility layer so that it could work, but this is something that we would have to work in at some point in the future depending on available resources. In any case, I am creating the internal ticket to record this request.
In the meantime, I mentioned another issue with the Toolset Image block, and this is also a factor here. Right now all image sizes—including standard or registered image sizes—are being treated as custom sizes by the Image block. Hence why you are running into problems when trying to use standard image sizes (or the 200px size that you registered).
So, I've attached that ticket to this thread.
When that issue is resolved we'll be able to re-test and I believe that things should then work smoothly providing you are using registered image sizes rather than custom sizes, but we'll have to test to know for sure.
That ticket is included on the board for the current dev cycle, I can't say exactly when it will get worked on but it is near the top of the pile.
I appreciate your patience, I realise it is taking a while to get to the bottom of this.
In the meantime, I expect changing that plugin setting should help.