OPA2604 is the only JFET opamp coming to my mind that can run on ±22V. A genuine one, because a "rebranded" TL072 could blow up
It may be cheaper to add 15V regulators and get a wider choice of opamps.
I frankly have no idea how discrete transistors compare to those in bipolar opamp input stages in terms of current noise. If they are comparable, a bipolar opamp ought to have some advantage over discrete due to about 10x lower input bias current. Whether it will be sufficient for you I don't know.
Yes, you would connect IN+ of each channel to the signal and IN- straight to OUT. Some 47-100Ω resistor between OUT and the cable to the preamp board may be a good idea to avoid risk of oscillation. Add 100nF ceramic plus a 10-100uF electrolytic between V+/V- and that should suffice for a quick noise test. I'm not even sure if it makes sense to upgrade to separate capacitors from each rail to ground later, the output current is very low.
And I came up with another option: if you set volume to max and balance to center, the preamp board will probably be more or less shorted to the input jacks. So it will see whatever impedance the external source has. So you could set the volume to max and use an external box with a low impedance (like 5~20k) volume pot. Or even an active preamp or whatnot.
It would take exerimentation to see what input impedance can be tolerated. So take some resistors and insert them into the RCA jack (from hole to ground) and see how much hiss remains when you turn volume up. Don't touch the input jacks with volume at max