Noise Matching transformer
Less than one ohm with leads-  I imagine that represents a big thermal load on the cryostat.

Yes, a room-temperature transformer can make a tremendous improvement. The important thing is that the Johnson-Nyquist noise in the windings does not contribute too much noise, so there needs to be enough copper.

There are commercial products that go up to the 10s of kHz, with noise in the 100pV sqrtHz range, I'm not aware of higher frequency units (but we have a product with a custom transformer optimized for 100's of kHz). Your desired frequency range is extremely wide- it would be easier to deal with in two ranges.