My opinion is to keep the HDMI connection and leave the output on the STB at 1080i. My reasoning is that the TV will deinterlace the signal to 1080p, so the only reason to do it before hand is if you can do it better somewhere else. I don't think that will be the case if you convert the STB signal from digital to analog, then pass it to the Yamaha to convert it from analog to digital and deinterlace it, then pass it to the TV. I also don't know if the STB can output 1080i in an analog signal (didn't look up the manual), so you might have to add into that the process of downscaling in the box, then upscaling in the Yamaha.
So - my vote is to keep it the way that it is.