I'm not sure there are many pre-existing designs, but NY Dave's MILA has good possibilities.
A 1:3 transformer has a 1:9 impedance ratio, so a 150 ohm source would have an impedance on the secondary of 1350, assuming a perfect transformer. In order for the electronics to add only 1dB of noise to the inherent noise of the microphone, it would have to have a total noise resistance of about 1350 / 4, or about 337 ohms. Assuming a bypassed cathode resistor as in Dave's design (or a negative bias supply feeding the grid), and ignoring the plate resistor for the moment, the main noise source would be the tube's own electronic noise. This is equal to 2.5 / gm, where gm is the transconductance in Siemenses. Turning the equation inside out, the gm required for an equivalent noise resistance of 337 ohms is 2.5 / 337 = .0074S, or 7400uS. That's high but not unattainable.
In reality, primary and secondary windings will have DC resistances; the secondary winding resistance gets added to 1350, and the primary winding times 9 gets added to 1350, so the actual impedance at the secondary is higher. That means the tube can be just a little bit noisier, which in practice would be perhaps the noise from the plate resistor. So if you design a tube stage with a bypassed cathode and operating conditions set to yield 7400uS (umho) of transconductance, the noise performance should be good.
Peace,
Paul