I'd advocate fitting new parts where you can in this case. The logic is that the extant parts are either serviceable or they are not. In the latter case you are better off without them inside the hub and in the former case they will be perfectly adequate spares for future use.
FWIW I am a big fan of adjustable cup and cone bearings but I have no time for that particular incarnation; in fact I think the arrangement is just plain stupid.
In any cup and cone hub the axle gets compressed when the QR is tightened, and this needs to be allowed for when adjusting the bearings. In most hubs you can either adjust the bearings with the wheel in the frame and the QR tight (eg some campag, some miche etc) or (using a special tool) you can adjust the bearings with the QR preload on the axle (pretty much every cup and cone hub in times gone by). In the current shimano hubs you can do neither thing.
The net result (IME) is that the bearings are usually set too tightly by about two notches in the toothy adjuster. If you try and check for free play it is rather tedious (you have to refit the QR skewer and tighten it on some (dummy) dropouts to apply the preload) and you still might not detect the free play correctly. The bearings have a good finish which means that overly preloaded bearings are not noticeably stiff to turn; it is easily confused with seal drag. Too much preload causes the bearings to fail, usually by pitting of one or other cone.
Anyway in many such hubs you have loose balls on the right side and clipped balls on the left side. I recommend loose balls both sides.
When you rebuild your hub be mindful of the possibility that any fragments of broken cone might be lurking inside the hub, so the old grease needs to be cleaned out thoroughly.
FWIW you can assess what is going on inside the hub by looking closely at the pitting using a powerful magnifying glass or (better) a low power microscope; if the edges of the pits are rounded, then the damage is old and may not be getting worse at a rapid rate. However if the edges of the pits are sharp, the damage is recent. If there is a mixture of edge types, some are old and some are recent, so the damage is ongoing.
Note that if you are ever forced to use a pitted cone, you usually can do, provided
a) the bearing preload is not excessive and
b) the damaged part of the cone is facing upwards, where it oughtn't see any service load.
To facilitate the latter, you can make a mark on the cone to indicate the damaged area and you just need to make sure this is facing upwards when the wheel is reinstalled.
cheers
