After a few tweaks on the volume control, I find that the 11 o'clock position on my main amp now gives me moderately loud sound

I just bought one of these to connect my iPhone to a 1968 Magnavox stereo console where I had to turn the volume way up on the Magnavox to get decent sound.

This boosted the sound

This does a great job boosting the sound from my TV to my amplifier

I didn't realize I needed some kind of amp to boost the sound coming out of my projector into the speaker system.

This worked perfectly and produced clean well detailed sound and fixed my problem.