I was basically in your situation about 4 months ago - a bit alarming to say the least. I was referred to the docs at aviationmedicine.com and they guided me thru the process to get a Letter of Evidence that I could pass one or more of the FAA-approved alternate color vision tests. There are about 7 or 8 acceptable color vision tests, and the FALANT is one of them. The others are mostly booklets of plates, but each one is a bit different and even though you might fail one, you may pass a different one. If you can pass any of these tests, you can get a 'Letter of Evidence' that you can show to your AME when you go in for a medical - it is proof that you meet color vision standards and you don't need to pass the AME's color vision test to get an unrestricted medical (assuming everything else checks out OK). The light gun test should be a last resort - "Plan A" should be to try and pass some of the approved tests with an eye doc.
The difficult part is finding somebody that can administer some of the alternate tests - it's often tough to find. I was referred to Dr. Monaco in Wilmington, DE who is an aviation vision expert and who has access to all the tests. After I passed a few of them, some paperwork was generated between Dr. Monaco and Dr. Snyder at Aviationmedicine.com, and within about one month I had the LOE in hand.
It cost me some $$, but the situation was resolved quickly by the experts. With 4000 hours and several types, you are past V1 in your career and it might be best to bite the bullet, spend the cash and/or go to the trouble of travelling to a place where you can do some alternate tests and get the paperwork done right. Just IMHO. Feel free to PM me for the details of the process I went thru.
Check these out:
www.aviationmedicine.com/colorvision.htm
www.flightsight.com is Dr. Monaco's site