I don't think that is it.
It sounds like there are multiple rooms of audio wired in parallel going back to a single head end location with a single set of stereo connectors.
So, with 12 speakers (assuming 6 rooms), that does NOT mean 6 zones, but it is ONE zone with 6 volume controls and a total of 12 speakers.
To run this, you should not use an A/V receiver, but should use a amplifier.
Like this:
http://emotiva.com/upa2.shtm or this:
http://cgi.ebay.com/Sonance-2120T-Amplifier-PARASOUND-CLASSE-KRELL-LEXICON-/150566042212?pt=LH_DefaultDomain_0&hash=item230e6f7a64
You don't want a surround receiver to run your distributed audio stereo setup. It's not designed for that and that is why what you have isn't doing it.
I've seen, more than once, home builders not properly use impedence matching product as well, so if you continue to have issues, you may need to pull out every volume control in every room and ensure that it is an impedence matching volume control.
It's worth saying, that this is about the worst way possible to do distributed audio and will provide the lowest quality.
The next step up would be to pull those binding posts off the wall and see what is wired up behind it. If ALL the speakers are run to the back of it...
Like this:
http://www.parts-express.com/pe/showdetl.cfm?Partnumber=300-542
Then, you can put in a few of these:
http://www.monoprice.com/products/product.asp?c_id=104&cp_id=10425&cs_id=1042503&p_id=3326&seq=1&format=2
Then run it to a 12-channel amplifier designed for home A/V distribution like this:
http://cgi.ebay.com/NILES-SI-1230-12-CHANNEL-AMPLIFIER-/200577211306?pt=LH_DefaultDomain_0&hash=item2eb3555baa
From there you get into the possibility of multiple source selection options, multi-zone preamps, and RF controlled solutions.
All of this should not be sitting under a 'counter' but should have been run to a dedicated head-end location which was accessible and properly vented. But, you take what you've got and make the most of it.