Basically in summary I have a high power, high turns ration transformer that needs a SRF of higher then the 20KHz upper frequency band. Now I am looking at nanocrystalline (linked below).
The core material itself does not resonate, and any resonant effects will be due only to a combination of inductance and parasitic capacitance of the actual windings themselves.
There are some time proven techniques to winding inductors with high SRF, and the key to this is reducing the capacitance and voltage gradient between adjacent turns.
One method is a simple single spiral coil, which is probably the ultimate, but often just not practical.
A classic example is the ubiquitous EHT transformer winding in old CRT TV sets. These have thousands of secondary turns, and typically about 1 Henry of secondary inductance and also require a very high SRF to work during the short horizontal flyback period, as well as a very high voltage rating.
Another solution is honeycomb or wave wound coils, and these are often broken up into multiple sections along a common core. Old style vintage RF chokes were often wound this way, and had surprisingly high inductance with high SRF.
If you are into really high power, another solution might be to use multiple smaller transformers with the primaries in parallel, and the secondaries in series.
The advantage is the turns ratio of each transformer can be kept low, and if you use a large cross section core, few turns will be required keeping the SRF high.
For instance four 4:1 ratio transformers so connected would produce an overall ratio of 16:1 without needing to have sixteen times the turns on one secondary winding.
The SRF of each transformer should be very easy to keep high, and the overall SRF combination would be no lower.
It may also be easier to design and wind (for example) four 500W transformers than one 2Kw transformer.