Beautiful theory destroyed by cruel fact. If you want to diddle physicists you have to propose experiments that cannot a priori be refuted because they contradict no foregoing observation, thereby prying open a gap between math and reality. Literature references help your credulity and your knowledge base. One-pass superradiant nitrogen and excimer lasers aren't coherent.
Coherence occurs in both time and space.
Free-electron lasers are accessible, but electrons are stable particles. Energy and time and are inextricably inversely linked. You are going to need a medium with a VERY high gain, because there isn't time to propagate an attenuating signal very far. It sounds kinda iffy to me. A good experimentalist can still beat the pants off a good theoretician.