OK! Great to have the photos.
Sorry to say first thing, but that is definitely a challenging room. I doubt you'd go for building an actual enclosed space within that basement

It could be done, and it could be a nice, cozy size for a small, totally dedicated theater of around 13' x 18' or so, but I get the sense that's not really what you have in mind.
So you've got the louvred door as the entrance to the utility room in the back (behind where you currently have your TV). Unfortunately, by code, the door to the furnace room has to be louvred, so there isn't a heck of a lot that you can do about the sound escaping from that back room into your large basement space. In other words, if you want good isolation from that noise within your theater, you'd pretty much have to build a dedicated theater room within the larger space. There's no real way to block the noise coming from the back room.
What you can do though is move your theater area further away from that louvred door and back room. It's not much, but it's a bit of a help at least.
I'm assuming the two doors on the opposite side from where the TV and louvred door are lead to the bathroom and bedroom? You could certainly do some extra soundproofing on the party wall between the large basement space and those two rooms. Solid core doors - or better yet, exterior doors with a sealed jam - and a layer of Green Glue and 5/8" drywall over the existing drywall will add damping and mass to that wall to help reduce sound transmission. But you were saying that in a year's time or so, you won't have anyone living down there anymore and that keeping those rooms quiet won't be as big a priority, so I don't know if soundproofing that wall would be of any benefit to you.
The dropped ceiling is a fairly easy fix. You can simply use acoustic tiles to help block some of the sound travelling upstairs. Since it's a drop ceiling, you have easy access to the ducts and pipes running through the entire ceiling space. You should consider damping them with something like
QuietCoat so that they won't carry the sound upstairs quite as much.
In terms of layout, you are definitely limited by the way the walls are laid out as well as all those cladded jack posts. To be honest, the best layout I could come up with that uses the exact room that you have now with no additional construction or changes would be as follows:
I'd go with a corner setup with the display straddling the corner formed by the 27' wall shown in photo #1 and the 13' wall that would be on the right hand side in photo #1. So you were saying that you were thinking of moving your setup to put the display on that 13' wall. My idea is similar, but with a corner diagonal arrangement, rather than a traditional arrangement with everything parallel and perpendicular to the walls. Take your idea for the 13' wall placement and rotate everything 45 degrees to the left
No you can heavily treat the corner that would be behind your corner-straddling screen with thick bass trapping. And place absorption on the 13' wall and mirror that absorption on the 27' wall. You can use the Acoustimac or GiK "Art" panels to make it look really nice
Your seating is now going to be diagonal as well so that you are facing straight at the display. The right hand side of the seating would basically be somewhere quite close to the support post that's on the right in photo #5.
As much as I love front projection, I think you could actually do quite well in this space with something right around a 10-12 foot viewing distance, which would make a 70-80" screen size ideal. That makes Sharp's 70" and 80" LCD displays a real option. The reason I bring it up is because if you keep the space open, it's likely there will be times when you want to watch something, but someone else wants to use the rest of the space for something else. With a front projector, you'd need the entire basement to be as dark and close to pitch black as possible for the best image. With an LCD, you can have the lights on and still enjoy a good picture
Honestly, I'd really need to know just how much renovation you'd be willing to consider. If building a new, enclosed space is an option, then a whole lot of possibilities for better performance open up. If you're basically keeping the basement as is, then I think this corner arrangement is about as good as it's gonna get.
Bass performance is going to be a real challenge. I would actually suggest that you go for something like HSU's mid-bass module + deep bass subwoofer split system. The idea being that you can place the mid-bass module very close to your seat so that you get all of the tactile impact without needing to turn up the volume very high. And then you'd have a larger subwoofer dedicated to only the deepest bass that you could place along a wall or in the corner to fill in the lowest octave.
Overall, unless you're willing to do a more serious build and renovation, I can see how you'll most likely need to be able to keep the volume level fairly low to avoid bothering the rest of the house. It's a pretty seriously compromised setup, but such is life

Planar speakers certainly make sense in this type of situation. The much larger surface area for launching the soundwaves means that the amplitude of the waves does not need to be as great in order for you to still hear all of the detail. This is what gives planar speakers their characteristic sound quality - very little movement of the surface that's creating the sound waves, but a large surface area. So speakers like the Martin Logans, Magnepans or Philharmonics do make a lot of sense. Combine any of those with a HSU mid-bass module and a deep bass sub - I'd actually highly recommend a cylinder SVS sub in your case since you could easily place it behind the display in the corner with the corner setup or lay it on its side to have it laying along the 27" wall. While your room size would normally call for the PC13-Ultra or the PC12-Plus at the very least, the fact that you'll likely be keeping the volume low means that the less expensive PC12-NSD will likely work well for you. One additional benefit of the PC12-NSD in your particular case is that it really drops off very, very steeply below 20Hz, which means that you won't get much of anything in the way of room gain of the subsonic bass that can easily travel through your house's structure and rattle walls upstairs. You'll still need to be mindful of everything 20Hz and above, of course, but you will eliminate the subsonic variable with the PC12-NSD. The PC12-NSD is also "unbreakable". So if you do happen to crank the volume, the worst you'll get is the limiter light lighting up on the sub. The sub will never bottom out, go into crazy high distortion or damage itself in any way. So it's a pretty good fit for your particular case. Not the norm for what I would recommend in this size of a room. But the right mix of features for your case in particular
