5998s are getting hard to find and expensive. Bottlehead doesn't sell them.
Stereophile did a review of the AKG 701 and it includes an impedance plot. That plot is quite flat, except at the highest frequencies; the inductance appears to be about 0.5mH in series with about 60 ohms. If the cans are designed for a low drive impedance, rather than the standard 120 ohms (similar to the Crack output with 6080 a tube), they might have a boost of 2dB at 20kHz due to that inductance.
In any case, response would be very flat up to 10kHz. If the boost is a problem, it can be removed with a simple Zobel, 62 ohms in series with 0.13uF, in parallel with each headphone. This will make the headphone impedance a flat 60-65 ohms at all frequencies
Not all headphones have such a benign impedance, but according to those measurements the 701 does.