I tend to use the 6J6 as a generic tube for use with our hybrid shunt regulator when some flexibility is needed. It draws a little more heater current than you requested, but you have the option of connecting one or two of the plates to the regulated B+ to adjust the cathode voltage to sit in the desired range.
Be sure to observe the 300V maximum plate voltage rating (the more contemporary Paramount soft-start circuit is regulated to 300V, so you're fine there), and the plate dissipation of 1.5W, which means that a maximum of 5mA per plate can be sunk through the 6J6. If you need to sink more than 5mA, tie the second plate in and you can go to 10mA.
With 300V on the plate and 1mA-5mA of current on one plate, your cathode voltage will fall between 7V and 12V DC, which is a happy place for the TL431 to operate.