Here's my beef. It seems that the smarter a digital camera is the dumber it is. I had a Canon 870 and I could get a good manual mode and set it to NORMAL or DAYLIGHT or I forgot what and set it a certain ISO and to a certain amount of seconds of exposure and keep it there for beamshot comparisons. Worked great. Well I tried to teach it to float in mid air in the kitchen and broke it.
Now I have a wonderful Panasonic DMC-ZS3. Problem is that it has little manual control and is missing my oh so used precise seconds of exposure time. So I can't do a proper beam shot of just any target under any circumstances. I have to pick something that is in the camera's range of likable scenes and distances and ambient lighting. I can get a setting of 10 seconds or 15 seconds but I need usually 5, 6 or 7 seconds.
From your beamshots it doesn't seem as though this is your problem. Exposure time looks good. The problem seems to be getting the beam to look like what your eyes saw.
This is where a flurry of discussions have occured. If your camera like mine can do a white balance setting (not AWB) you can set a benchmark. Some might say the sun is best. Some might say your benchmark should be a benchmark flashlight that many will recognize. What ever your benchmark is state it or lable it in the pic and most folks will understand what you are doing. Keep it set that way for the comparisons.
My Panasonic is difficult but if I set the focus to read a point and not an area, set the white balance to a benchmark and set the ISO to manual I can get the shot but it's no where as easy to do as with the Canon. Also this new camera doesn't do justice to perfect red light like the Canon did. A strawberry yes. A red light no.
I hope that helped a little. I feel your frustration. I've seen so many beamshots I can tell what your lights were doing so they are viable to me. Unlikely they, as they are, will meet the scrutiny of knowledgeable members. This you already know. Good luck.