Third time I am trying to write up this fairly extensive response, so I'm dumping your comments and hopefully it will work this time!
Your room isn't quite as bad as it looked in the first drawing. That new drawing really goes a long way to helping to understand your home setup.
Now, here is the reality of your situation:
The family room - DUMP THE SIDE SPEAKERS!
No, not really, but for the purpose of 'surround sound' you absolutely must not use or think about those speakers.
What you need to do is to properly break up your home into the separate zones you have.
Your family room currently doesn't have 6 speakers. It has TWO ZONES. The first zone is your main surround listening area. This consists of the left and right main speakers and the surround left and right speakers. You intend (and should) add a center channel and a subwoofer. This will give you a solid 5.1 audio setup.
Could you add more speakers?
NO! Surround sound has rules! You have to follow them if you want good surround sound. So, your room should look very similar to this when done with the surround sound setup.
Yes, the speakers are a bit high - up to you if you want to bring them down some in the front.
Now, I'm not ignoring the rest of the speakers in your home - but they aren't a part of surround sound. You have got to focus on JUST the surround sound and getting that right to start off with. One speaker to one matching channel output on your surround receiver.
Front Left, Front Right, Center, Surround Left, Surround Right, and the RCA connection for the subwoofer.
This leaves the surround back connection as well as the front height/wide speaker connections unused. THIS IS FINE FOR NOW!
Get all of this setup, then use the automatic room calibration microphone to get the setup completed for your surround system. This will give you an accurate and proper surround setup when you are sitting on the couch across from the TV enjoying a show or movie.
Now, let's look at the rest of your home and the 3 stereo zones you have remaining.
One stereo zone is in the family room, off to the side, and two other zones in other rooms.
This is where you use the SS6 and the SURROUND BACK output of your VSX-30 receiver.
From page 23 of your owner's manual (with some paraphrasing!):
Connect your SS6 to the surround back speakers terminal.
Select 'ZONE 2' from the Speaker System menu (page 105 of your owner's manual)
Once the SS6 is hooked up to the receiver on the zone 2/surround back output, you can connect the other three pairs of stereo speakers to the SS6 and enjoy stereo audio in any (or all) of the other locations. You can listen to any ONE room, or ALL rooms or any combination thereof at the same time! This system is not very limiting except for ONE key point...
The other rooms will be playing audio at the same volume if they are all on at once. Depending on the size of the rooms, this may not be acceptable and would be a reason NOT to use the SS6.
Instead, you probably should use a speaker selector with an integrated volume control for each output.
The Sonance SS4VC, for example, will do exactly this. It is identical to your SS6, except it only can handle 4 extra stereo speaker pairs, and it has integrated volume control.
So, your three stereo speaker zones get hooked up to one output each of the SS6/SS4 (whichever) as follows...
Input - From Surround Back output of your VSX-30 receiver
Output 1 - Family room stereo speakers
Output 2 - Room 1 stereo speakers
Output 3 - Room 2 stereo speakers
Output 4 - OPEN! Don't connect anything
Once this is all said and done, you will be able to listen to all 11 speakers in your home plus the subwoofer if you want to, or you can sit down and just listen to a movie the way it was meant to be listened to.
Don't confuse more speakers with 7.1 or 9.2 or anything like that!
For example, I have a 7.1 audio setup in my basement, and a 5.1 audio setup in my family room, and another 11 stereo zones of audio in the rest of my home. I can turn ALL my speakers on at once - but that does not make my home into a 34.2 audio setup! It makes my home a 7.1 setup, a 5.1 setup, and 11 stereo zones which all happen to be on at the same time.
Your home will be as follows:
Family room - surround zone - 5.1 audio setup
Family room - separate stereo zone
Room 1 - stereo zone
Room 2 - stereo zone
The nice thing is that you will be able to adjust your setup as you like and listen to what you like and you will be able to ENJOY your setup because you know it will be setup and working properly.
If you do decide you want/need more power to the other speakers in your home, you can go with an external multi-channel amplifier, like one of the ones I listed earlier. Yes, you called that overkill, but that is exactly what you are asking for - more power, so it may be appropriate at that point if you do need it.
Also, larger speakers tend to sound a lot better. I use 6" speakers throughout my home and they sound okay, but I've started using 8" speakers from Monoprice and I do find they deliver more bass and better response than the far more expensive Sonance speakers in the rest of my home. So, perhaps a speaker upgrade may be in order at some point.
Your setup is workable, and you have the gear now it sounds like, so why not just go ahead and get it all going? Just follow my directions, and you should have a system which you are happy with.