You could just get a single LM1084 linear regulator
I know the discrete BJTs aren't really necessary, but like I mentioned in the OP, a lot of the interest I got from the market I'd be selling in was in the aesthetic quality of the device. Tattoo power supplies are as much a fashion statement as they are functional, and the two cans bolted to the top of the case add to the visual interest. I suppose I could buy dummy cases, but that seems disingenuous.
Looking at some of the examples, it does seem like the LM1084 easy to implement for current limit/protection though, thanks.
Isn't a tattoo machine basically a DC motor and what you want is speed control? If yes, then using PWM to regulate the motor speed is much simpler and more energy efficient. Still there has to be some current limit and thermal shutdown but a modern PWM controller chip has that built in. If you still want to go linear then the chips suggested by Mariush are a good choice but you have to do the math on the cooling to see if you can get maximum current at the lowest voltage with a real world heatsink.
When dealing with any kind of power electronics I want my circuits to have 4 safety features: a real fuse, current limiting, thermal shutdown and overvoltage / reverse voltage protection.
Well, yes and no. There are machines that use solenoids, electromagnets and springs in various arrangements, BLDC-based devices with integrated controllers, and a few other designs. WRT the SMPS approach being more efficient, I'm painfully aware, but linear power supplies are favored for their performance characteristics, perceived or actual.
There's a real fuse on it, it looks like the lm1084 should be easy to implement for current limiting looking at some example circuits, that's probably what I'll go with. You only draw peak power on most tattoo machines when you're using fill needles, which need to be run higher to get clean punctures. Most cheap to mid-end supplies only claim 2A output, most rotary (Brushed DC) machines draw less.
Reverse voltage is something I'm still working on ATM, thanks to you both for the ideas. Glad to have your input.