What does one purchase after owning horns?

If I were you I would look for something like Blumenhofer or classic Tannoy speakers from the Prestige series.

Tannoy Prestige: you get the life and dynamics of horns with seamless integration between the high and low frequencies. Actually I find it hard now to listen to multiple drivers speakers after been accustomed to dual-concentric.

You should listen to the models with alnico magnets and pepperhorn: Kensington, Yorkminster, Canterbury or Westminster.

Soundlab ESL speakers are what you may be looking for. They are a point source speaker with perfect top to bottom integration.

This will most likely require an amp change also however.

Watch for a pair of Duo's or Duo Omega's.
The Duo's main horn goes deeper than the Uno's.
I almost gave up on the Duo Omegas that I purchased.
My room has a terrible hole in the 142Hz - 160Hz region.
Right were the horns and subs integrate.
I just could not get the bass right.
I tried reversing polarity on the Sub225's but it did not help.
Tried endless positions.
Then I bought a used Behringer DSP1124P parametric EQ for $80.00.
Ran a second pair of outs from my pre to the EQ then to the XLR inputs on the Sub225's.
I have a Behringer DEQ2496 that I use solely for RTA use.
A total of 3 left and 4 right parametric filters took me from listening hell to listening heaven!
If horns are off of your short list, I second the Sound Labs.
But keep in mind, that it may be the bass response of your room, not the speaker.

If you could go up a bit in budget the Audiokinesis Dream Makers would be worth looking into. If you prefer something more conventional then the Jazz Modules might work for you.