Both channels have the initial power-up pop. Only the right channel (I'll call this the good EF86 tube) has the secondary pop after a couple seconds. I think that no second pop on the left channel can be attributed to the EF86 tube on that channel (when I measure the KReg voltage, on power up, it starts at .25V and rises to .5V after 20 seconds). When listening, that channel is much quieter, has a poor noise floor of white noise, and some pops. I will wait and see if this clears up after more hours of burn in.
I can reconfirm that the level of the power on pops is heat related - if I let the Eros cool down for an hour, I get a single LOUD pop, and my Denon shuts down - there is no secondary pop, as the amp is already off. If I only wait 30 seconds after turning off the Eros before powering it back on, I get a much quieter pop, and everything stays on.
Thanks for all the help guys!