One additional thought is that since ESRI has partnered with Latitude Geographics, and their software such as Geocortex Essentials is designed to work specifically with ESRI ArcGIS software, and is now integrated with use of Web AppBuilder (WAB). There might be some potentially useful functionality there in custom WAB widgets to help solve the dilemma of dealing with 300 layers in on app.
Geocortex Essentials added a "Layer Catalog" capability to their software suite:
My coworker implemented this in one of his Geocortex Apps and it's pretty slick. You just open it and it enables "search layer catalog," or you can browse and select the layers you want to add to the web map from the layer catalog.
To give this a whirl and to see this in action go to the following hyperlink:
Oregon-Washington Data Viewer
Once the Viewer is launched, click on the Map tab <*hint: upper left corner>
Then click on the Layer Catalog button as shown in the screenshot below:
Select the layer, and add it to the map:
Maybe Geocortex will build this into a widget that will work in WAB, or maybe they already have. It might be worth looking into in this use-case.