Ok, let's see. First congratulations on a good build. I'm not surprised that it worked right off the bat. The vast majority of builds do. I, too, am impressed with the logical layout and the exceptional photographs in the Eros Manual.
Several of the official Bottleheads have stated that the cathode of the EF86 tubes needs to form, 40 hours is suggested. And I would think that this is what you are hearing. Hum can of course be from interconnects and ground loops as well but you have convinced me that the burn in is making the difference here.
Tube rush, the white noise you describe, is often a product of the tube. If it persists to bother you after the first 40 hours I would expect you would want to do a little tube rolling. The EF86 has the greatest impact on the sound but a noisy 6DJ8 could cause noise in both channels since it is the second stage for both channels. What I tried to say was that having rush from both EF86s is less likely than having rush from one 6DJ8. But you will want to try some other EF86s because of the impact on the sound that they have.
Here is a link to tube equivalents for the Eros:
http://www.bottlehead.com/smf/index.php/topic,1028.msg7556.html#msg7556Enjoy!