Do any sub $1,500 receivers do OSD/GUI over HDMI?

You mean the setup menu over HDMI? The 805 does do this indeed.

Denon AVR-3808ci

MSRP on the 3808ci is over $1500.

The 2808ci should do it for MSRP $1200.

What you're talking about is a step beyond OSD really. You're referring to video overlay. In other words, if you adjust while watching content you see the volume number on the screen without blanking the display to do so. Or by hitting some button you can see the surround mode, etc. Is this what you're shooting for?

I'm not sure if any of them do that just yet, though i AM sure than none of the Onkyo receivers do. They have OSD over HDMI, but to bring it up it fills the whole screen with a black background, and then switches back to your source when you're done. Not great for checking surround modes or volume level during a movie.

It's not entirely clear to me, but the Denon 3808ci ~might~ be able to do that. I believe that the Sony 5300ES is able to as well, though I've never seen a screenshot of either in action.

Hope that helps.

I got the 3808ci for $1450 from an authorized dealer in DC

Yes, the 3808ci definitely does do this. Over HDMI. There is a bug with the mute button, however, as "Muting On" does not dissapear from the screen after the 2 seconds or so that it's supposed to. Hopefully a firmware update will take care of this.

When switching sources, surround mode and input source are overlayed. When switching surround modes, the new surround mode is overlayed (about 5 secs.) Volume overlay lasts about 1.5 to 2 secs. Is overlayed a word? Looks strange.

Can't help you out with the 2808, but I doubt the GUI would be much different.

The harman Kardon 247 and 247 does this. OSD over HDMI as well as whic hinput you seleced + volume control with a white bar.

The Onkyo 705 does this, but only for transoded sources (HDMI sources are passed thru untouched). I thought that the 875 and 905 did this, having the Reon processor, but maybe not. The 705 does pass this overlayed volume control out over HDMI: but as I said it is only on analog sources (in my setup the only time I see it is with a component input from the Wii).

Keep in mind that most units that I have seen that do this have it as a menu selection in the set-up screen ("on" or "off") and when engauged will have some effect on video quality as the graphics generation (even when not in use , but in standby state) will undoubtedly have some negative impact on what quality (or even frame rate/type) of signal is sent out to your display....for this reason and in an effort to avoid the distraction that snaps people out of the alternate reality of the movie, I would recommend turning it off...if you need to be switching surround modes or adjusting volume constantly in a movie, you haven't been pleasantly transported into the alternate reality. If your equipment is doing it's job "play" should be the last button you press (except "pause" if you have to go real bad).

Playing too much with the gear during music, tv or music, just seems to make me think that you either have too many distractions or that you aren't happy with the sound. In any case, a character generator (even when off)overlayed on top of a pristine HD image is likely to cause unwanted issues with PQ.

"Overlaid" is what you are looking for. Looks a bit less funny.