I received my two boards - Epiphany 16 of course - and for each I soldered the link across J15 and put a 25 x 6.9 mm 5V DC fan in the standard Adapteva case. Using the Adapteva power supply, and connecting only Ethernet, and not USB or HDMI, each board booted, acquired an IP address, and then was able to successfully run matmul16 and the cycle count program for math operations. I haven't tried to run other example programs.
So far, so good, and I'd like to think things will stay that way... one board idles at 54C and the other at 57C. I use fan, heatsink, and Arctic Silver 5 (not the adhesive formulation, although I should have; with reasonable care I don't suppose the heatsink will be moving too far).
I see that some Epiphany example programs need to be built, the 2D FFT and etc., so the next step will be in that direction, as well as gingerly trying to connect USB and HDMI (at least some of the time).