"DEEP and extended" bass (by my definitions) is extremely rare in full range speakers under $2,000. Maybe something like the Def Tech models with powered subs in them might get you close to the bass you want, but I'm not sure what they run new.
If you could somehow work out a Martin Logan setup, I would not even think twice about it...
Martin Logan Ascent i's... $1975 
... but then you need a center and a sub. With the exception of the deep extended bass, you described these speakers very well and I can tell you I've not heard anything better in my lifetime. And I don't just say that because I now own them, I really mean it. My ML setup really does it all and someone needs to knock me clean between the eyes if I ever get rid of my ML speaker setup, other than to replace it with the same after it wears out.
Here's the
Def Tech BP7002's for $1299...
Of course those are used.
In the new line you could look into the Paradigm line and probably pick up a very capable front stage for under $2000.
I was impressed with the
Cambridge SoundWorks speakers...
You could get a very nice setup with them for your front stage and have money left over for a nice sub as well.
Another option is the
Axiom line... we just picked them up as an affiliate. They are very well respected.
There are sooooo many really good options.