I think I found a bug in the api for creating subplugins for the External Tool (LTI) activity.
In order to make the subplugin appear in the activity chooser, one must implement a function called get_shortcuts(), which is going to substitute the function get_types(), now deprecated:
When you follow the instructions given in the documentation above (implementing the deprecated get_types() function), you are able to get your subplugin activity displayed in the activity chooser along with the original External Tool activity.
However, if you implement the get_shortcuts() function instead (this function should return a set of propierties a bit different, as stated here: https://github.com/moodle/moodle/blob/master/mod/lti/lib.php#L219), the activity chooser only shows the lti subplugin, while the original External Tool activity dissapears from the list.
Please, vote for this issue: https://tracker.moodle.org/browse/MDL-60223