I started dabbling a
bit with one of these last year. Not for coin photography as I have a
good, portable, light-box that gives excellent results. I tried it with a DSLR while photographing a symphony orchestra rehearsal. I found the colour temperature of the LED's was very heavy on the
red and it was difficult to get a
good white balance. Of course, there are LED's and LED's as you are aware. The colour temperature will vary with the
quality of the LED. Also, I used it on flash setting and think it may have been better to be on permanently, but haven't experimented further.
Did you operate on flash or permanent and did you have white balance problems? I notice you mention the result can look "unnatural". Your experimenting with mixing light sources is interesting. I used to do the same before the light-box. The ambient light of indirect sun will also impact on the results. What you get one day is not what you'll get the next. A completely dark room gives better control over light source but it is rather hard to see little coins. Also, as noted, the spectral qualities (how they reflect light) of bronze and silver vary. Coin photography really s difficult.
I experimented with the various light source adjustments available when processing RAW files. It wasn't fully satisfactory and further colour processing was necessary to reduce the
red end of the spectrum. All this processing is time consuming - and time wasting - hence my delay in experimenting further.
I've been meaning to experiment with the light for videoing too but haven't got around to it yet.