You hold them in your hand (wear a glove) while you clean them with the angle grinder.
You can use baking soda to blast the combustion chambers and ports clean, pistons too. Or you can use paint stripper to remove the carbon. Or a combination, paint strip most of the carbon off, soda blast what remains. Soda blasting is excellent for cleaning the piston ring grooves. The valves are hardened steel so you can just wire wheel them clean once you have them out.
Cut strips of rags, oil them, and thread them through the guides before you start your cleaning.
You got your valves somewhat clean but not completely. I told you, that carbon is really hard and baked on there. Time for the knotted wire wheel in the 4 1/2" angle grinder. You'll want to clean the backsides of the valves as well. Get all that crusty build-up off all the way up to where the stem meets the guide.
The seats on your exhaust valves are badly carboned. Pic 11 in your 1st set clearly illustrates where that valve was leaking between the sections of built-up carbon. You can see the streaks the exhaust gases left behind. Wire wheel all that crap off. Once the valves (and their seats) are TOTALLY clean, you can move on to the lapping. Make sure the seats in the head are clean as well. You don't want to be lapping carbon, you want to be lapping steel.
You might try threading a good bolt into that stud hole to check the threads. JB Weld may work. All you can do is try I guess. You have a steel stud going into an alloy head. Chances are, the head threads are going to give out 1st.