That might work I would discourage the chaise on the sectional just do an ottoman same sitting comfort but much nicer seating when you company. IMO thi s is ahuge space that is poorly laid out the DR table needs to be about 3x the size I would put it infront of the patio doors off the kitchen then you would have a huge LR with a couple of seating arragements one in front of the fireplace and one for T.V viewing all pieces that can be moved when you have a crowd.We have a large LR and I puposely bought piecs that could be rearranged for different looks and purposes like the Christmas tree for instance .So I have 2 sofas, a chairs that do not match the sofa or each other but work in the space a long bench that can be moved easily wherever I need it I really dislike sectionals because they are so site specific and in your space I think if possible think many useful pieces that can move easily .

Unfortunately, our other potential space is our living room which is small. I'd like to keep it upstairs as the finished basement is the playroom. Good suggestion, though. I pushed the chairs back towards the fireplace a little more and it's not bad. Is it an issue that the sofa isn't centered on the TV? Do I need a larger area rug? We may change the carpet to some type of faux hardwood, so I think an area rug still makes sense. Would a coffee table look good with this arrangement is the two end tables? It would be centered on the sofa, which would be off center from the TV.

I moved the couch to the other wall, is this better?

If you want a TV in that room the only place it can really go is to the right of the fireplace (maybe to the left if you find that works better for you). It is never recommended to put it over the fireplace unless there is nowhere else for it to go. You have more than enough space on the right for a nice console. Maybe in the future you can do something more dramatic with the fireplace as it looks small in that large wall (or maybe you are already and it's not finished yet). Put a tall piece of art over it (something that is less wide than the fireplace). Face your sofa toward the fireplace and TV. The dining table should have the long side parallel to the slider. I can't imagine it fitting the other direction. I don't think it's a bad thing to have your old furniture in there for a while. It will help you get an idea of the right size for new pieces. You may also get better advice if you post a graph paper drawing of the space so the commenters know exactly how much space you're working with. The perspective in pictures is sometimes misleading.