I would de-sludge the engine. Look up Kreen. Works great. Follow the directions. After that I would run at minimum 10w30. I have heard people extending the motors with these exact symptoms with Rotella 15w40. You need to keep the oil pressure above 25psi at idle.
Some info from answer.ford.
Different expert here, you do have codes for both sides of the engine, P0012 is for bank 1 (passenger side) and P0022 is for bank 2 (drivers side) usually when both of these codes set it is more than just a solenoid. Usually there is an oil feed pressure concern that will also cause the cam phasers to stick even if the solenoids are ok. I work on 3-4 of these a month when were busy and 90% of them need engines because the crankshaft thrust bearings wear and the front crank journals wear and cause excessive pressure bleed. Not to mention the cam bearings, phasers, VCT bodies and chain tensioners.
These engines are notorious for phasers and VCT solenoids sticking from oil feed problems to the cylinder heads. Cam sensor codes do not mean the sensors are bad. They can be set by any timing drive component that is making the valve timing incorrect due to over retarded or over advanced cam timing due to a sticking or inoperative phaser/VCT. The bad or sticking phaser or VCT solenoid is usually the result of the problem not the root cause. Here is a list of what I check or replace on these every time I get one in with phaser noise, VCT codes, cam sensor codes or misfires caused by VCT issues. Before any disassembly the PCM data pids for VCT error correction should be monitored to confirm it is a VCT issue. If the vehicle won’t run, a compression test can also verify the VCT problem.
Oil Pressure. Any thing under 25 at idle will cause phaser issues. Oil pressure needs to be steady and not fluctuating. If low or fluctuating suspect crankshaft thrust bearing wear. This can be verified by a simple end play check. Also if engine is sludged in the least amount there could be oil starvation to the valve train which is also very common on these and can be verified by pulling a few cam caps on each side, it will be obvious if the there is an oil supply issue to the valve train by the condition of the caps and journals.
VCT valve body/solenoids. Have seen many issues with solenoid plungers sticking and restrictions in valve body due to plugged or collapsed screens.
Timing chain tensioner gaskets blown. This will cause oil pressure bleed to the valve train and affect phaser functionality.
Camshaft phasers sticking due to contamination or low oil volume/delivery pressure.
Crankshaft endplay, I don’t bother fixing the engine if endplay is over .010
Oil pump, I change if there was any evidence of sludge or varnishing. There are passages in the pump that clog and can cause oil starvation problems.
In short if I don't find oil pressure concerns and my cams are in good shape I usually replace the phasers, VCT bodies, oil pump and tensioners on every one of these. Ford has updated these part numbers several times with improved engineering designs.