Nearly all HDMI receivers can accept LPCM over HDMI. You can power the z640 speakers with an AVR. The plugs it uses are RCA, but the output is not line out, it is regular speaker level. So that means your every sentence is wrong, but you come off sounding like you're stating facts... so help yourself and best of luck!
From a FAQ about getting 5.1 from a Wii U.
"I have an AV Receiver with an HDMI input. I'm guaranteed to get surround, huh?
Maybe. As well as needing an HDMI input on the back of your AVR, it must support LPCM 5.1 over HDMI. Some older HDMI receivers only accepts LPCM 2.0 (so you will only get stereo). Some AVRs just do HDMI pass-though, which is video only. Check your AVR user manual to confirm it supports six (or more) channel LPCM via HDMI."
So, while I think anything recent (few years) would work fine. Some older ones only do LPCM 2.0 and some were just pass throughs.
Edit: Just looked on craigslist and found a STR-K7000 w/ 5 speakers and some stands for $75. Sounded good but guess what, the receiver is just a pass through when it comes to HDMI. It cannot extract any sound from HDMI connections. So don't assume LPCM 5.1 works on all old HDMI receivers you find.
The z640 center channel doesn't have an RCA jack and neither does the sub. Only the L, R, SL, SR connect via RCA. They connect to the RCA jacks on the sub which I believe houses the amp. The center channel connects to the sub via a special cable to handle volume, fader, etc. The only way to connect an AVR would be to connect it to the 3.5mm jacks like you connect them to a sound card. The problem with connecting them via 3.5mm to RCA converters to an AVR is the z640's inputs are only designed for a few watts a sound card would put out. I would think an AVR's much higher watts per channel would cause problems.