$_CB_framework->displayCmsEditor calls JFactory::getEditor() which calls Editor::getInstance(). We call the display function of the editor on display, which calls the "onDisplay" function of an editor plugin. That's all we're doing. It's a pass through function. We are not touching the editors parameters in any way beyond sending input name, input value, width/col, and height/row.

TinyMCE loads editor specific settings, including styling, in onDisplay. JCE appears to load this in onInit, which shouldn't really be a problem. The problem seams to be how JCE detects what editor to use where. CB doesn't use Joomla content events since they're not relevant to CB so if JCE is depending on Joomla content events that could be part of the problem. JCE function getComponent doesn't seam to have any issues finding CB on CB views though.

Investigating further to getProfile in JCE responsible for compiling the list of available editors. The problem comes from "User Group" and "Users" parameters. If both are empty the editor will never load. So if you select an extension in "Components" and don't specify "User Group" or "Users" it won't work. The validation in backend is missing for this which means you don't get an error for making this mistake. It's not even clear those parameters are required, but at least one of them is in getProfile.

With the above information I set "Components" to "comprofiler" and "User Group" to "Public" and the editor loaded perfectly fine throughout CB. The only issue I see now is "Editor Layout" works partially, but for some reason there's a "display: none;" style on several of the toolbar rows preventing them from displaying yet they are there and function. Only the Default editor works right in my tests across multiple extensions (this issue was present even in Joomla articles).

My tests were done on a clean install with latest release of JCE. I've no issues getting the editor to load specifically in CB by setting "Component" and "User Group" parameters correctly. It's also possible there's a load order conflict in JCE it self. Try ensuring the component specific editors are ordered before your default editor. My only issues were with toolbars having "display: none;" on them, which was not a CB specific issue as tested a custom editor specific to Joomla articles and it did the same thing.

The other extensions you noted are likely using Joomla content events since those events are relevant. Joomla content events are not relevant to user profiles so we do not fire them and it JCE is depending on them for its loading behavior that will be a problem. JCE should be doing all this behavior in onInit or onDisplay, but it's not from what I can see so I've no clue where it's doing it exactly. In my tests getComponent worked correctly and output CB and getProfile worked correctly outputting the CB specific editor with its correct parameters so I don't know what else to suggest.