5.5v LED Power Supply
I picked up a new 5v 5A industrial power supply to handle the LED's. With it hooked up to my voltage meter, I trimmed the potentiometer to set the output voltage to 5.5v, splitting the difference between my ChameLED's and the CoinTaker LED's voltage designs.
Powering up the LED's with this new power supply, the difference was night and day (or more like night turned into day, that's a lot of light!). The 6.3v CoinTakers now look fantastic, nice and bright and with almost no flicker at all when PWM dimmed. And of course the ChameLED's are still bright and beautiful with absolutely no flicker! I'm not really sure why the CoinTakers has a minor bit of flicker, but I expect it is due to their fully-rectified AC/DC design, though it could be because I'm still slightly underpowering them.
I put my ammeter on the new power supply with all 76 LED's lit up, and I recorded 4.4A, so it's safely within the 5A capacity of this tiny power supply. Looks like I got a winner. This also means that, on average, I'm now pulling about 58mA per LED, though I haven't yet retested the ChameLED vs. the CoinTaker to see how each performs.