No it won't. The lower, the better. That preamp must have a cathode follower output stage, which will make it a good performer during high-power demands.
I would try to follow the "eight to one" rule and mate it with an amp with a VERY low input impedance. But, I don't know of any amps with a 4k to 5k input impedance.
Nonetheless, a low input impedance will allow your preamp to be "a good performer during high-power demands" like Aball says.
YBAs are, usually, 27k. You could even biamp with those! And feed them well. (Because you'd, still, be sending your signal into 13.5k).
Maybe, there's a complementary German amp you should explore. . .
The 8 to 1 rule is being misunderstood. It should be viewed as a "minimum" rather than a fixed value - and even then you are on shaky ground. Most of the circuit topologies are voltage sources so decoupling by means of low output impedance and high input impedance is mandatory to cut down on the interaction between them. The reason the ground remains shaky is because speaker interaction is even more important and tends to swamp out the more-minor effects between electronics. The only way to determine if two components work well together is to try them because it may not even be electrical interaction that is the problem - it may be human/electronic instead!
ET - The noise floor problem you encountered wasn't due to the cathode follower but rather, the high gain and high input impedance. Some amp designers feel that higher input impedance is better (for the reasons I just mentioned) but the downside is a rise in the noise floor. And high gain just magnifies normal tube noise (mostly Johnson noise and vibration-based feedback). This high gain didn't come from the CF but from stages before it because CFs don't have any voltage gain. The byproduct of CFs is current gain due to their transconductance nature, which is to say their main effect is to lower the output impedance to maintain the integrity of the voltage signal waveform into the next gain stage (amp, etc.), also for the reasons I mentioned above.
Stoned - all this means your preamp will work fine with any amp, so long as you like its type of sound. Enjoy!