Denon AVR 3313ci Zone 2 sound delay

Denon AVR 3313ci Zone 2 sound delay
I am a novice so please don't assume I know what all the abbreviations are in your response.

Here is what I have:
Denon AVR 3313ci
Main zone room - Polk 5.1 speaker set up in main zone (only use 5.1 so that I can have a zone 2 - see below)
Other rooms - Two Polk speakers with wall OSD volume control in several other rooms.
I have Cox HD digital cable DVR (Scientific Atlanta Explorer 8642 HDC) that provides much of the audio/video content we use.
Everything works fantastic in the main zone. There are a few things I am either doing now, or planning for the future. But here is my immediate challenge.

Now: Our house has an entertainment/pool table room (pool room) adjacent to the main zone room. I have speakers in this pool room and, for now, want to simply have zone 2 audio in this room. My DVR is connected to the AVR by HDMI. I initially plugged my zone 2 speaker feed into the Denon surround back (assignable) terminals, assigned them to zone 2, and expected zone 2 sound. Only after hours of frustration and research on this site and others did I realize that these terminals will only pass analog audio. My DVR has every type of output immaginable, and I tried them all, but unfortunately, I only got audio in zone 2 when I connected the red/white RCA cables between the DVR and the AVR. This was disappointing, but would still be OK for what I am doing now. An example of my application is that I want to hear the football game audio broadcast loud and up close in the in the pool room while other people are also watching and listening to the same game in the nearby main zone room. This all works fine with one MAJOR issue. The sound coming from the Zone 2 speakers is a few fractions of a second ahead of the main zone sound. Since the two rooms are adjacent to each other, that tiny audio output offset undermines the value of having a zone 2 in the first place.

Objective: Determine some way to get main zone and zone 2 audio snychronized. Anybody have any ideas at all? I am willing to try anything. Even options involving pre-amp out where I have to buy another power source or something may be worth while. But I don't want to go to that extreme without knowing that is a viable solution.

Well, thanks for the advise about reading the manual. Don't worry, I did not take that as a slam.
I am an engineer and problem solver, but not not one involved in electronics, or anything remotely related. Unfortunatly, sometimies that means I am compelled to try and solve all problems myself, instead of hiring and paying an expert. In reality, I am the kind of user that spends a bunch of time figuring out how to make things work for what I want to do, then once it works, I move on and never worry about it again, until at some point years later when I want to do something different. Me messing with my audio/video needs now is the result of me moving into a new house and also buying a new AVR. Since my previous set up in a different house with a much earlier model Denon did not expose this delay, and since the interworkings of AVRs is not where I spend my free time, this issue was not immediately obvious. Now back to the issue.

So, since the speed of sound is 768 mph, and my main zone and zone 2 are seperated by 20', I have ruled out the sound travel time as the reason for the delay. When I changed both the main zone and zone 2 output source to Pandora (i.e. not passing through DVR and not converted to analog) the delay is gone. As you said, this suggests that perhaps the output timing difference between the DVR HDMI out and from the RCA out are the source of the problem. I am looking for suggestions on how to overcome this timing offset.

Now that was direct and definitive advise from jdsmoothie. Thanks. I got excited and immediately changed video mode from "AUTO" to "GAME". The fired up zone 2 again, and unfortunately the delay is still there. Maybe ever so slightly less delay, but can't really tell for sure. Any other thoughts?

Do you think it is the difference between analog signal and digital signal that is causing the delay? Or is it more due to just not have full HDMI connection from beginning to end? My older 2nd AVR does NOT have HDMI, but does have optical input and the DVR has optical output. That is a digital signal, right? If I connected DVR to 2nd AVR by optical, then connected zone 2 speakers to 2nd AVR, would that achieve the same objective that you have suggested?