Jon,
Honestly, when I first read your post, there were just too many questions regarding matters that are pretty subjective and I didn't feel like taking the time to write out a detailed response. But since you didn't get any other responses, here are a couple of thoughts.
First of all, understand that your questions regard home theater applications and the majority of interest on this forum is two-channel music listening. That is probably why you are not getting the response you expected.
You ask about running the preamp and amp outputs of your Pioneer receiver. I would think that you can probably do both at the same time but I don't know without reading up on that model. I suggest you read through your user manual to see if that is possible or you post that question on a forum relating to home theater receivers. Most people on this forum don't use receivers to power their Martin Logan speakers. They use separate pre-amp and amps because of the high-current needs of Martin Logan speakers.
You then ask if you can mix powered and unpowered ML speaker or design-series with ELS-series. The short answer is of course you can. For that matter, you can mix ML speakers with Bose speakers. The question is will you be happy with the sound and that is a completely subjective thing. Some people will be thrilled with it. Others will hate it. Only you can really answer that question for yourself. There are those on this forum who absolutely feel that Martin Logans are not appropriate for home theater applications. There are others who have full Martin Logan five or seven channel setups (me included) and love it.
One option to consider is getting the best center and subwoofer you can afford (say a stage center speaker and a depth or descent subwoofer) and then skimp a little on the main speakers (getting a pair of Sources or a used set of Claritys) and powering it all with your Pioneer Receiver. This would give you the most bang for the buck where it matters for home theater (center channel and sub) but it would suffer a little as far as music listening goes. Ultimately, you would be better off in this case to use your Receiver as a preamp and get a separate amp to power the speakers, for reasons explained below.
Another option is to go all powered across the front, with a pair of Puritys for the mains and the new Feature powered center channel. Then you would just use your Pioneer as a preamp/Processor and disable the amp part of it. Assuming that if you did this you couldn't use the amp to drive the surround speakers, you could get an inexpensive two-channel amp to drive those speakers (such as the outlaw audio 2200 monoblocs). But it may be (and probably is) true that you could use the preamp outputs for the Main L, R, and C channels, and still use the amp outputs to drive the surrounds.
Both of these options are fine. Is one better than the other? Not necessarily. Are there other perfectly acceptable options? Sure. There are many possibilities depending on your budget, your needs, your ultimate goal, and your tastes. The problem with asking which is "better" is that, if you get any responses at all, you will get five different responses telling you five different things which are the "best" way to go. A lot of it really is pretty subjective.
Since you aren't really listening to much music, I would focus on the center channel and subwoofer. Those are the most important speakers in a home theater application. If you don't wish to purchase a quality high-current amp (like a Sunfire - just for one example) I would consider going with powered speakers across the front. Martin Logans generally just don't do very well with receivers. They have a difficult capacitative load that drops down to one ohm of impedance at high frequencies. Most receivers just don't handle this load very well.
If you can afford it, the Stage center channel with a pair of Vista for the front left and right would make an awesome five channel theater system, along with the rears you already have and a good subwoofer. But you would absolutely need to get a better amp to drive them. Whether or not your Pioneer is adequate as a pre/pro at that point will be up to you. Martin Logans do have a bad habit of revealing the limitations of upstream components. When I first bought my Ascents, I powered them with my Yamaha Receiver, which I had been very happy with driving my Definitive Technologies speakers before that. Once the Martin Logans were in the system, the Yamaha had to go and I moved on up the quality chain. They just ruthlessly reveal the limitations of lower quality components.
On a side note, if I went this route (Stage and Vistas), I would purchase a seven channel amp that was either 200 wpc or, preferably, 400 wpc and use the extra two channels to biamp the Vistas. If you went this route, with a Depth or Descent for a subwoofer, you would be amazed at the sound, and would probably end up listening to music on your system a whole lot more than you expect. But you would be blown away by the sound for music or movies. And your wallet would be hurting for a long time.
So, as you can see, it really depends on what you are looking to get, and how much you are willing to spend.
