I believe you need to unplug (or "terminate") the HDMI cable. Why not simply connect the HDMI cable to the TV (or component video to the TV) and have a digital audio connection to the AVR. You can then either use the TV only or the AVR. You may need an analogue audio connection from the STB to the TV for audio. If using HDMI you need to use the analogue audio connection "associated" with the HDMI input on the TV.
You didn't mention the make/model of the TV or AVR, but the above should work with most. Also, a Harmony remote may come in handy so that you can do the switching automatically. One activity could be "watch TV" while you set up another activity for "Watch TV with AVR". I have set up a lot of people to do just this without two video connections to the TV.
The following thread goes into additional details. Apparently it is possible to have CV and HDMI connected if the HDMI is "terminated". Perhaps turning off your AVR does not terminate the signal.
Parry, but one component video connection (with analogue audio cables, which you'd need as you discussed in post 1 anyway) from the STB to the TV and one HDMI connection from the DVD player to the TV directly accomplishes the same thing. Please reread my post and I've added a paragraph at the end. Most people simply turn on the AVR all the time. After all the sound is better.
Hugh, see the link in the last paragraph of my previous post.
When the projector is off, the component video is still not active.
The linked thread discussed having something between the STB and the TV to terminate the signal, like an HDMI switch, or an HDMI AVR (essentially the same as unplugging the cable). I would guess that powering down the FP fully may achieve the same? Perhaps you could check by unplugging the FP and if that works, connect it to a switched outlet or power bar? Don't know if that would have any adverse affects on the FP.
Considering the quality of the picture typically required on the Slingbox, you could perhaps consider S-video, composite video or even RF-coax, which are always active on the STB?