WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
Building, troubleshooting and testing of these amplifiers should only be
performed by someone who is thoroughly familiar with
the safety precautions around high voltages.
I have no idea if it has been tried. I can see a 6EJ7 in the 2nd gain block role of a passive EQ phono preamp. A CCS loaded 6922 in the 1st gain block role should provide enough gain to get past pentode partition noise effects.
Look at the data sheet. Notice that both gm and RP are high. A DC coupled voltage follower is needed between the 6EJ7 and the O/P jack.
There have been many preamps (phono&mic) that have used pentodes. 6AU6, 5879,EF86/6267,6J7 etc. Most of these were originally designed for these applications,and some had low noise/low microphonic versions available. The 6EJ7,and it's 'brother',the 6EH7, were NOT. These tubes were designed for extremely high gain in intermediate frequency amplifiers in television sets and other tuner applications,in an effort to reduce the number of tubes and tuned circuits and therefore reduce cost. Most,if not all examples,are horribly noisy.They were never intended for audio work,and these problems have no effect in their designed for application. I had the same idea as you many years ago,as I did a great deal of work for recording studios,and had on hand dozens of these,mostly NIB Amperex.We were trying to find substitutes for the other types,as they were very hard to get at that time. Complete waste of time and effort. You may get lucky and find a quiet one,but that'll be a total fluke!