John- Are you sure you don't want to transfer to the University of Illinois?
I'm passing your questions on to some colleagues and will post their answers when received.
Meanwhile, I've heard the first issue discussed occasionally, and am sure that the equivalence principle still works but forget how the argument about the integral of the radiated fields over time works. I believe that the second question has a simpler answer, since you're really asking about the changing density due to changes in relative velocity with respect to the medium. Unlike the electron gas or the microwave background fields, however, the vacuum fields can be Lorentz invariant, i.e. look exactly the same regardless of nominal velocity.
Aha, a colleague confirms my answer to the second issue and writes of the first issue:
This problem is generally considered to have been solved by Boulware:
“Radiation from a uniformly accelerated charge”, Annals of Physics 124, 169-187 (1980).
His abstract says:
The electromagnetic field associated with a uniformly accelerated charge is studied in some detail. The equivalence principle paradox that the co-accelerating observer measures no acceleration while a freely falling observer measures the standard radiation of an accelerated charge is resolved by noting that the radiation goes into a region of spacetime inaccessible to the co-accelerating observer.
However, this has been contested by Parrott: http://arxiv.org/pdf/gr-qc/9303025
, published in Found.Phys. 32 (2002) 407-440.
I think that the issue concerns the end effects. "Uniformly accelerated" requires an infinitely long time interval in both the past and future.
(published on 01/26/10)