Yes, I've noticed this before, when designing a noise source. Also think in terms of voltage, rather than current. I think you'll get more noise by using a current source, rather than a a voltage source and resistor.
Does anyone know if it's temperature dependant? Would making the current source NTC using transistors and diodes, rather than stabilised using a voltage reference, be beneficial?
You'd have to map out the e_n vs I_r vs T space. Maybe it's consistent across production of a given part, or across parts, but who knows.
Regarding impedance, it's not very important. The equivalent source resistance is whatever the dynamic resistance of the diode is. As long as you aren't loading that heavily, you aren't losing much signal. Or loading it by half to get ~maximum power point, whatever.
A lower impedance would be desirable to increase bandwidth -- rather than allowing the voltage to jump down randomly, keeping it up, making it more likely to spark soon after, again and again. That would also allow higher bias current, to some extent. Which is really to say that the Rz will be lower in turn, but probably about the same power noise density.
Tim