It is an all-too-common misconception that UNJ internal threads have a radiused crest. They do not.
The "J" thread form is a modified thread form with a controlled, tangent root radius on the external thread, and an increased minor diameter on external and internal threads. It is usually specified in aerospace of in fatigue critical applications.
The sole modification to the internal thread form/dimensions (when compared to a “standard”, “non-J” thread) is a small increase in the thread minor diameter (the “pre-tap” or “pre-thread-cutting” diameter) to prevent interference of the radiused external thread root with the internal thread.
Example: The minor diameter of your 1.125-18 UNJEF-3B thread should be 1.0784/1.0709, where the minor diameter of a 1.125-18 UNEF-3B thread is 1.0730/1.0650.
UNJ internal threads can be inspected with standard threaded plug gages (of the appropriate class). The (modifed) minor diameter is inspected with a gage of the apporpriate size, or directly measured to the applicable requirements.