Very small room systems and synergy

Lets not be hasty here. It may be that what your are hearing has little to do with Metal Dome Tweeters.
It's likely that the overall sound is characteristic of combined effects.
Amplifier / Interconnects / Position.
"  What I find is a lack of overall frequency response "
This sounds like you are right on track with concerns of Placement.
Re-Set for Near Field Listening to ensure that you can evaluate the sound accurately.
Varying the distance between the two mains should help discern a difference.
No personal experience with KEF though all input indicates a refined
highly regarded Loudspeaker.
I think that an Amplifier will make the difference.

What I would say is that to some extent. Is that cost is a limiting factor.
The Current Technics Line Up is quite good and priced at three levels.
Though don't give up on what you have until you have you can evaluate and hear the difference yourself.
A local HiFi dealer should be helpful for demo gear and evaluation in
your system.
After checking out (reading about) both NuPrime IDA8 and LS50. 
I think that both choices are outstanding.
But $1000 for an integrated is A Low price Range.
Although I am coming down on the side of Hybrid Integrated.
And that L/R Mains Position and Set Up are of great importance!
Also note that Planar Magnetic sound is very different sound field than 
Dynamic Driver Set Up.
A SubWoofer could be used to reinforce Low End.
If no one will believe me then refer to below video.
https://www.youtube.com/watch?v=cTnituQu8ig