1) What do you do to clear out the gunk and use the compressor just to supply air again? Hold it over a garbage can, trigger the valve and hope for the best? Compressor is still under 60psi of pressure.
2) Is the gunk a one and done supply or can it be used subsequent times (particularly if the first time no flow happened)?
3) Under pressure, the device knob will also not switch from gunk flow to air flow setting.
I've never used my Clarity's tire repair kit (although I just changed the tank of slime and will send my unused, just-expired-but-refillable tank to anyone who asks for it before April, 2024). However, the Owners Manual answers one of your questions.
It says not to use the tire repair kit in these situations:
• The tire sealant has expired.
• More than one tire is punctured.
• The puncture or cut is larger than 3/16 inch (4 mm).
• The tire side wall is damaged or the puncture is outside the contact area.
• Damage has been caused by driving with the tire extremely under inflated.
• The tire bead is no longer seated.
• The rim is damaged.
For your question 2), bullet 2 indicates the slime tank is a single-use proposition.
I didn't know your item 3), that the Air/Repair knob can't be turned to the Air setting when the hose is still connected to the valve after using the Repair setting. Did it make a mess when you unscrewed it? If so, that's what Honda decided had to be the case. I'll be putting some rags in the compartment with my tire repair kit to wipe up excess slime.
So if you can't turn the Air/Repair knob when the kit is under pressure, you have no choice but to perform your procedure 1): unscrew the hose from the valve, switch to Air, and blow out any slime remaining in the hose. Then you can switch to Air, reconnect the hose to the valve, and pump more air into the tire, if necessary.
I hope I never have to use my tire repair kit. Your experience was worse than I expected it would be. Please accept my condolences.