Late to all this, but own a P20000 that had a head clogging issue last year:
1/ Yes, do a manual clean, the one that puts the head over to the left side of the printer (as you look at it, away from capping station) and do a manual clean underneath, with the wiping swab-sticks dipped in head cleaning solution. There is an online plan somewhere with which head area = which color. DM me if you can't find it - I have it here.
2/ My issue turned out to be a bad ink cart that was not pressurizing properly - it cost me many hours and tons of other inks, before I pulled the cart, looked closely, and found the tell tale stain around the end of it. Epson tech support immediately recognised it for what it was, once I sent photos and a purchase receipt - no arguments, and replaced it plus a good number of extras, gratis. Didn't really make up for all the days/ ink, paper lost before I figured it out, but... immediate resolution of the issue.
3/ If you truly need a new head. Don't spend $4000+ on one from Compass or whomever. Buy a complete P10000 - they are (were?) only $5000 after rebates, use the exact same head, parts, etc, so have your tech take that off there, plus you'll have all those free extra parts - capping stations, wipers units, etc, etc, thrown in. Its wasteful, un-environmental, and ridiculous - but that's the Epson model. Sometimes its cheaper to buy a new razor, than a pack of razor blades.
4/ Use an indie tech - there's plenty around. Not sure where you are, but I have East Coast names if useful.
Good luck!