You know, you are sounding experimental and creative right now. What about a DIY build in any of those categories? Check out Madisound, Meniscus and Parts Express for ideas.
You can build 3 different types of speakers for the budget you have, and in many cases buy cabinets or have them made for you.
As a long time DIY'r, I couldn't agree more. DIY is a great way to end up with speakers that will sound as good as commercially available speakers at at least 5 times the money spent.
My current, and maybe my last pair of speakers, are the "Bordeaux" designed by Curt Campbell and Jim Holtz.
They use an Aurum Cantus Aero Stricture tweeter (similar to an AMT), and a Accuton ceramic mid in a semi open baffle array. And 2 8" Dayton woofers per speaker in a standard ported enclosure.
I have a total of about $3000.00 in them, which includes flat packs for the enclosures. And the end resulting sound quality is easily comparable to commercially available speakers at around $15K.
The Parts Express forums are a good place for technical help, but tend not to get very high end.
And unfortunately, Meniscus Audio went out of business over a year ago. It is too bad, since they had some quite high end kits by most of the well respected designers.
Another great source, is Troels Graveson from Denmark. All his designs are pretty high end, but I don't believe he has any designs that will fit the OP's requirements.
And lastly, a guy who has a pretty controversial reputation here, Danny Ritchie. I helped a friend build a pair of GR Research, NX-Otica, their 2nd to top, open baffle speaker kit.
And anyone who says Danny is a charlatan, I doubt have ever actually heard one of his speakers. Because these kits are under $4000 including flat packs, and they sound substantially better than anything close to their price.