OK. 0.35mV then- you are going to have difficulty with a 6DJ8-based phono section. The problem that you run into is that 6DJ8s, 6922s and the like aren't designed for audio so you run into noise and microphonic issues which at the very least color the sound of the preamp.
The 6DJ8 is difficult also from a design perspective as it has a mu (gain) of about 33, which makes it a medium-mu triode. High-mu triodes, like 12AT7s and 12AX7s, allow for high gain with low noise and low microphonics; IOW low coloration.
If I were you I would not worry about the tube type so much and concentrate more on who has a tube phono section that can handle a moderate to low output cartridge like you have. If it doesn't use 6DJ8s you can always put them up on eBay...