My Demo results: I feel like I'm at a frustrating block in my speaker journey

First of all, it’s a miracle that anyone is able to gain any meaningful advice from posts like these, with so many different opinions being offered that ultimately steer you in a hundred directions at once. A lot of people don’t pay attention to what question is actually being asked by the OP or they offer ridiculous solutions that will almost certainly not be implemented for a multitude of reasons. You’ve had several of these posts already in this thread but it is a systemic problem throughout the forum for sure. It’s just a consequence of having an open forum where everyone can offer an opinion regardless of its relevancy. That being said, I think several people have made some good suggestions for you.

I personally own the ML 35XTi speakers and they were paired with a Marantz 5011 AVR when I first started out a few years ago, so very similar to your setup. I thought the MLs (bi-amped) sounded great with the Marantz, especially for around $2k total investment. I also used the system for 2.1 home theater and it saw a lot of movie time so the AVR worked out well as it offered built-in room EQ and easy hook up for everything.  It sounds like you might be at the point where you’d like to take your listening experience to the next level though (just as I did), and if so I would suggest looking into two things: the placement (room layout) and the amp.  I think people are correct in mentioning the room layout is less than ideal but this happens when you have a system in a general use family space and not a dedicated room. It is what it is. So you just have to find solutions. Rather than say something silly like “you need to get those speakers out 3 feet from the wall” I would simply suggest that if you are able to rearrange the room at all in order to free up some space between the left speaker and the chair it would certainly help.  It doesn’t have to mean completely switching the seating locations. It could just involve moving the stand and speakers to the right a bit. If the TV has a fully articulating mount this may be an option. That’s assuming you have space to move to the right. If not that’s fine. At that point I think it would be wise to only consider bookshelf speakers you could raise high enough on stands to clear the chair arm so you don’t block the output from that left speaker. I also like the idea of wall mounted or even in-wall speakers. Given the room challenges I think an on-wall or in-wall could be a great solution. It all depends on whether you can modify the room layout or not and whether you want to mount something in or on the walls. Room treatment may be able to help as well given how close the left wall is to the speaker and it being a pretty reflective environment but this being a living room I’m sure you don’t want to add a bunch of wall treatments. You could look into an area rug perhaps if that’s something you and your wife wouldn’t mind. Maybe even a picture or two on the left to help a little with reflection. Nothing glass obviously but more like a thicker canvas print. The art panels are great from companies like GIK but it depends on how much you want to spend. You could even do curtains on the left window if that’s something you wouldn’t mind. 

As for amplification, I think you could find a number of solutions for a modest sum that would offer improvement.  The Parasound suggestions are good but that would also eat up a lot of your budget unless you find a great deal on a used one. If you were only focused on buying a new integrated with a $3k budget then sure. But if you’d like to stay at $3k total for any new purchases there are several integrateds that could work well. The Cambridge Audio CXA81, Yamaha A-S801, Musical Fidelity M3si or M5si, Peachtree Nova 150 or 300, NAD C 368 or 388, Marantz PM7000N all have good build quality, built-in DACs, respectable power, get great reviews and most importantly they don’t suffer from the AVR design limitations.  Without having to worry about 5-11+ amplifier channels, a ton of video and audio connectivity options, bass management, etc. the integrated amps are able to focus more on sound quality. It really all depends on how you use the system and how much connectivity you need.  If you just need 2 channels of amplification and a DAC and maybe 2-3 sets of RCAs at most then the integrated amp could be a great fit and one that will probably take your listening enjoyment to the next level up.  Most of these are under $1500 new so that also leaves money for speakers. The 35XTi is currently on sale for $400 each, which is a steal. I know ML makes a wall mount model in the same series too that you could consider. I’m sure other people could make suggestions for reasonably priced on-wall or in-wall options too. However, if you don’t want to mount anything on the walls or cut the walls to install in-wall models then the ML 35XTi or even the Focal Aria 906 might be what you’re looking for. I think trying to do what you can with the room or at least with speaker placement will help a lot and combining it with a more purpose built integrated amp will be even better.  I don’t think you’d be unhappy with either speaker option at that point. Good luck with your journey.