I think the general advice on that was to fill those slots with cheap tubes - like Electro Harmonix, though used Sylvania 6SN7GTB could fit the bill too (and should last a LONG time). I'd hate to leave the slot empty or covered in tape.
A pair of 6SN7 in some kind of follower configuration, probably output coupled via electrolytic capacitors, does not make a super headphone amp by today's standards. But it still might sound nice with high impedance headphones like Sennheiser HD600.
Tube designs which use transformer coupled outputs can use basically the same circuity for preamp and headphone amp outputs. The problem for OTL (transformerless) amps is providing enough capacity on the output caps to not roll off bass when driving headphones, while also not compromising the cap choice when used as a preamp that doesn't need very much capacity. That's hard (if not impossible) to do well. So Cary made the choice to use a separate output stage just for headphones. The problem is it's probably not up to par with the preamp stage.