Okey dokey.
Well first off, it's a good room in the sense that it's rectangular and closed off (ie. not an "open concept"). On the down side though, it has cathedral ceilings, which are, acoustically, a bit of a nightmare
You're dealing with something in the range of 2000-2500 cubic feet, which is a decidedly "medium sized" room. This is definitely a room where I would use a subwoofer rather than relying on tower speakers to handle all of the bass. If the budget were a lot higher, I'd be going for two subwoofers and quite a bit of bass trapping, but clearly, for now, that is not in the budget
I'm very very tempted to try and find a way to get you some acoustical treatment into that room though. Honestly, acoustically treating that room will make a bigger difference in sound quality and any speaker upgrade. What you can do though is to "hide" your acoustic treatment budget into the "decor" budget
I'm sure your wife is open to dressing up the room a bit. Try and get as many plush, absorbent materials into that room as you can. See if you can swing some big, thick drapes to go over the windows. Some nice, thick carpet for the floor or a nice, thick rug if it's hardwood. If you can find a way to put some leafy plants in the corners or have leafy plants hanging overhead, that will also help as those will work to diffuse the sound reflections.
If your wife is saying no to running speaker wire of any kind, I'm prone to doubt that she'd be supportive of "egg crate" sound absorbers plastering the walls, or 6" thick bass traps lining the corners

But you can usually get away with things like plants, drapes, rugs, wall hangings and bookcases and you might even be able to "trick" her into putting those into the decorating budget rather than the home theater budget
I can see right away why you would like the Klipsch sound in that room. The horn loaded tweeters are more directional, so you are getting less reflected sound, which makes them sound more detailed and clear than a lot of other speakers in that same situation.
I'm struggling a little bit to figure out why surround speakers are a complete no go. Your room is certainly capable of supporting them and they would work well in an enclosed room. There are a ton of options for flat speaker wire hidden under the carpet, hollow baseboards that can carry the wire while making the room look upscale or flat, paintable speaker wire that can perfectly blend into the baseboards. It sounds as though you've had this discussion already though, so I won't beat a dead horse

Still, perhaps your wife just isn't aware of all of the many options that are out there now.
Sticking with only Best Buy makes this a bit difficult. You're really only looking at Klipsch, Polk or Def Tech. Out of the three, Klipsch would likely be my top choice for your room as it is.
The key to the whole system though is the subwoofer. To be honest, I'm most tempted to recommend that you keep your Klipsch B-3 bookshelf fronts. Add to them the matching C-3 center and then get yourself a darn good subwoofer.
To me, this would be the most efficient way to get a really good sounding 3.1 setup in that particular room (along with the "hidden" acoustical treatments that I mentioned).
The B-3 are capable bookshelf speakers. Obviously, not the "greatest in the world ever"

But for your budget, you wouldn't be looking at any sort of massive upgrade anyway. Your current center and surround speakers do not match up in output or quality though and neither does your current sub.
So since this is a 3.1 system anyway, it makes the most sense to me to get the matching center to your existing fronts. That will even out the front soundstage and give you good detail and dynamics for the mid-range and higher frequencies.
Then, it's up to the subwoofer. As I said, this is the key to your whole system and a good sub, in that room, will bring the whole thing together and really give you a full and powerful sound for your movies.
In order to do that, I'd have to recommend going with one of the internet direct brands. Right off the top, the SVSound PB10-NSD jumps out as a terrific choice, but considering your budget, I think I'd have to give the nod to the
HSU STF-2
The STF-2 is appropriate for your room size and a very accurate and capable sub. It'll blend brilliantly with your B-3 fronts and C-3 center. Just be sure to experiment with placement to find the very best location and be absolutely sure to sit it on top of a
GRAMMA riser.
Simply put, if it were me in your situation, this is what I would do. The focus for me really is the subwoofer. After that, it doesn't make any sense to me to spend significant money on speakers that would essentially be a sideways move. You already have capable front speakers with the Klipsch B-3 bookshelves and the Klipsch design actually suits the needs of your room quite well by limiting reflections and enhancing detail. Giving them their matching C-3 center counterpart will bring your entire front soundstage to life.
Best of luck!