I am not sure what is blocking on your install.
These issues do not happen locally or on other installs, hence I suspect either Theme/Plugin conflicts or the Server is also involved.
What I can surely tell is that the development site you shared presents several very slow queries, specially when it comes to AJAX, wether backend or front end.
And that can be due to the server.
As well something is
I took the liberty and have set up what you elaborate as your goal on the development site.
Instead of "Dealers" I created a new Post type "Toolset Dealers".
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Then I added 2 Fields (just one for the test- a phone number and an address field):
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Then I added 3 Dealers in the post type and filled all information.
Then I added a View, and queried that Post Type, and added a Map as output:
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After, I added this all to a Page:
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Initially it displayed the map in the ocean.
Then I applied our own API key and it displayed all the pins on the map as expected, with all the info as expected.
What was unusual during all this process is that it took 40 minutes.
Usually this takes 10 or less. And that was due to a long lag of server response I experience on the development site.
Loading a GUI as example (those pop ups) takes forever, and that is not expected.
What I can imagine happened with the existing View is that due to the lag in response, one clicks several times on several settings and items.
This then can corrupt the database settings.
I suggest to ask the Server Admin what causes the slowness on this site, as with Toolset also this is not producible.
I suspect there is some sort of error logging going on that slows down the site, or the server provides a very low bandwidth only.
The View I created seems to work fine.
Can you confirm?