Thanks for the reply Robert. We are actually not trying to use two Web Maps with the same map object, just allow the user to configure two of them in the application template. Our application supports multiple languages and what we are trying to do is have the user create two Web Maps, one in English and one in an alternate language. Then we load the default web map and when they toggle languages, we destroy that map and create another one with the other web map id. This part actually works really well, the part we are having troubles with is ArcGIS Online allowing multiple web maps to be configured through ArcGIS online using the Web Map Dialog picker. This way our users do not have to download the codebase and configure it manually themselves.
P.S. Parsing the operational layers works pretty well, we are doing that to create a custom TOC widget to control the layers from the web map plus some defaults that we added, and when we change web map id's, we just re-render the TOC (it's a React component), and it works perfectly with the new web map.