Short version: as of 6 May 2015, Epson is providing v1.10 for the Home Cinema 5010. I can provide it to anyone who doesn't want to deal with tech support, though in my experience it was quick and entirely painless.
I've experienced the blinking blue power LED/high fan/lamp never comes on problem a handful of times since I bought my 5010 in 2012.
Typically, I'd give up after letting it sit that way for minutes or hours, then unplugging and trying again a few times. The longest this ever went on was 3 evenings, with the projector unplugged during the day in between - eventually, it would fix itself. At least once (and maybe every time, I don't recall), I got the double blinking red, which went away after an unplug/re-plug cycle, and then everything was back to normal again.
Two weeks ago, it happened for 4 nights in a row, and I finally got annoyed enough to dig the PJ box out of storage to find the 'Private Line' card, and called Epson. Of course, I decided to do this on a Friday night, and as luck would have it, the PJ fixed itself shortly after and worked fine through the weekend (and the week since).
I ended up calling on Wednesday anyway, and was able to quickly reach a tech - they didn't even ask for the Private Line PIN, which was nice, since my warranty had expired about a year ago.
They sent me firmware version 1.10, which installed without any problems over my old v1.03. Of course, since the PJ was working normally again anyway, I won't have any idea if the new FW fixes the problem unless it happens again in the future.
The zip file they sent me--via a third-party website, "Hightail"--included the 1.10 FW, plus a PDF file with instructions, the FW updater utility, and a custom USB driver. As someone who's used computers for >25 years and written software for >15, the custom USB driver was super sketchy, as was the VB
script that the updater utility required to be run first under administrator privileges to register some custom software library. (.OCX I think? I'm not on the machine I used for the upgrade right now.)
The custom USB driver lets the PJ pretend that its USB port is an old-school COM (serial) port. I guess they didn't want to spend the extra $1 or so per unit and just use the standard USB serial port emulation chip?
Anyhow, aside from the sketchy software stuff, I was able to upgrade the FW on the first try, and the PJ started up normally (as it had anyway for the last several days). The service menu now shows "110" at the end of the "P" version string, as expected. So, it would seem that 1.10 is now the latest version for the 5010 - and also the 5010e and 6010, according to the instructions PDF.
My zip did not include any release notes, however, which it sounds like is typical lately? I read through a few dozen pages of this thread, and earlier posts spoke of receiving release notes, but later posts, like the latest before this one, seemed not to have gotten them.
Regardless, if anyone wants the v1.10 firmware, send me a message and I'll forward it along. There's no way for me to tell if it fixed the problem for me, since it fixed itself before I installed the new version, but it doesn't seem to have caused any new problems of its own. I also have yet to notice any differences in behavior or picture quality between 1.03 and 1.10.