Well if it's just two variables this is easy to deal with. In the C2 runtime it's very simple - I just deleted those cached variables and make SDK calls every time they're needed so they'll update correctly. This is done for the next release and shouldn't need any code changes to third-party addons, the official plugin will just update automatically.
In the C3 runtime it's a bit more complicated because it can run in a web worker in a different context to the Instant Games SDK, so it does need to cache the variables. To allow them to be changed I've added some methods to the official Instant Games plugin so callers can change the variables. I'm not sure if anyone's plugin supports the C3 runtime yet, but in case you need it, the relevant calls are:
// Must check plugin used in project
if (C3.Plugins.InstantGames)
{
const igPlugin = this._runtime.GetPluginManager().GetPluginByConstructorFunction(C3.Plugins.InstantGames);
const igInst = igPlugin.GetSingleGlobalInstance().GetSdkInstance();
igInst.SetContextId("...");
igInst.SetContextType("...");
}