Best Speakers under 1k for me

Hey guys, so my birthday is coming up and I want to put some money towards a new speaker purchase. My current setup is Chromecast-Topping D30-LM3886 Chip amp (in progress)-Q Acoustics Concept 20.

I've been hearing great things about the lxmini's and Zu audio Omen. My room is about 11x13ft and one half of my front wall is a double pane window. I can build another amp pretty cheaply for biamping.

What do you think? I'd prefer to not use a separate subwoofer.
There is a guy on here that is selling a set of Zu Omen Mk ll for $800. The thread is "Zu Audio upgrade". I have recently bought a pair. I am enjoying them. 
If your thinking Zu I’d recommend the Dirty Weekends when they’re available. For $999 they are exceptional and you probably won’t need a sub. 
The Emotiva T2’s are pretty great for the price, they just aren’t everybody’s cup of tea asthetic wise, as they look like studio monitors.

I would suggest going to the Zu audio website. They compare the Zu Omen Mk 1, Omen Dirty Weekend Mk ll and the Omen Mk ll.
I bought Omen Mk 1 used for $300 and am planning a driver upgrade that Zu Audio offers for 699.00. They refund $200, upon the successful return your old drivers. Also there is always someone there to answer your questions.
I have a NAD C326BEE that I'm powering them with. The combination might be a tad warm for me, but I think I can fix that with a change in amplifier and I plan to upgrade the drivers. I saw these speakers initially on craigslist for $500.00 and the guy kept marking them down. I had never heard them before until I went to his house to demo. Now I'm a fan. When I've been home, they've been on constantly. I am now looking for a new integrated to pair with them. I might try tubes. Maybe build a SET amp.
My favorite system of all time was Dahlquist DQ-10's with a Dynaco Tube amp. I am hoping that these speakers and an amp change might get me back... but much more efficient.
If you have drywall try In wall speaker where you get full advantage of infinite baffle and no font wall boom or reflections. Elac Debut IW-6 (4inch deep) claims same cabinet speaker performance. but toeing in and determining the placement is difficult before installation, it has to be planned before cutting the dry wall. room behind may experience leaked sound. you can try drywall it self turned slightly to face the listening position.
Also read this in wall speakers there are you-tube and web to help.
Having just left RMAF, all I can say is Dali Oberon, which is a brand new line of speakers.  The Oberon 7 floor stander they demonstrated absolutely blew away everyone I know who heard them.  The bass from these things is practically subterranean and the mids and highs were great as well.  If you can stretch to $1,400, they are a no-brainer.  No sub needed for these babies.  They also have a smaller Oberon 5 floor standing model. 
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Thank you so much @ashoka that's the sort of "outside the box" advice I was hoping to hear. As for everyone else, I'm really frustrated because I feel like my room is responsible for my lousy sound so my (rather uneducated) assumption is that buying other box speakers is going to give me more of the same muddy, bright, headache inducing sound in a different flavor, is this a fallacy on my end? 

As far as the in wall speakers, unfortunately one of my speakers is in front of a window so that's impossible with my current setup. Is DSP perhaps the solution?
@Ashoka thank you so much, that was the sort of "outside the box" advice I was really hoping to hear. Unfortunately one of the locations they would be installed is the double pane window covering half my front wall, so not possible with my set-up.

I'm seeing a lot of recommendations for monopole speakers, I feel like my room is responsible for the muddy, bright, headache inducing sound I'm hearing currently, could switching to an Open Baffle design help?

I just feel like switching my box speakers out for other box speakers will just give me a different flavor of the bad sound I'm hearing now, is this a fallacy on my end?

Very Grateful,
Those Dali Oberons are gorgeous though, shame their not active. Seems like DSP crossovers are the way to go nowadays.

Kef LS50w looks very tempting, and I can spend my amp budget on that.
Hi , interesting post . How high is your ceiling ? Do you have carpet ? Cloth covered furniture ? Have you tried hanging a couple blankets for a test ? Sounds like you need to address room issues first . I have MK I Omens and love them . My room is 18x20 with a vaulted ceiling and very thick carpet . I have heavy drapes and a huge cloth covered sectional . As far as Zu’s people either Love or Hate them . I have a sub , but don’t really need one . Have you considered an inexpensive tube amp kit ? I rotate between 12 wpc and 60 wpc Tube gear . I’ve also used a vintage Marantz SS receiver and a Modwright 200 wpc integrated . Your question is best answered by Zu, email them . When I contacted Zu about amps , Mr Sean responded  the next day ! I can share pics and a boatload of experience, as I bought used Zu’s and then spent $10k building a system around them . Message me and we’ll talk . Regards , Mike B. 
For under $1K? Maybe a different path would give you better results. A Mac. a good sw (e.g. JRiver), and a pair of HomePods would sound excellent. You can pick a pair of HomePods for $300 each at Costco. They will beat any cheap speakers under $1K and possibly under $2K.