Sorry! 99.9% chance it's time for a full timing job. Remove front cover and put in new Timing Chains, Phasers, Chain guides, Tensioner arms, Tensioners, Crank Timing Gear, Oil Pump, and gasket set, and remove / clean both VCT solenoi bodies and oil pan / pickup screen. Use _ONLY_ OEM phasers, Melling high volume oil pump. Do it right and your truck will be good to go for another 150 - 200,000 miles.

 

I'd look at the fpdm above the spare tire first. If corroded, it can cause your intermittent problem. Also, much cheaper and easier to fix than timing. Also wouldn't hurt to check the charging system... Bad alternator or battery could throw funky codes.

 

 

Yes you should check the fpdm on rear axle .Very high failure rate .Might as well change fuel filter if its not new .
You are not receiving the bad timing codes yet but you are in the zone . The timing parts are much improved .
Right now I wonder what plugs you used and if plug job done correctly . This engine very fussy about that . Should be using sp546 not the troublesome 515's You have misfires on bank 1 pass side. That does not mean that you are not having misfires on drivers side but maybe below the threshold of setting cel ..Mode six will tell you raw counts per cyl .
You should clean cyl sprk tip to get carbon out of there with carb cleaner as it breaks plugs . Plugs should be done hosp clean with new boots . Clean all connector plugs with contact cleaner .. Replace all connectors that don't lock on . Clean cop contacts real well . Torque all plugs in 25 to 28 foot pounds' . Very hard to diag engine unless you start with a real good tune up .
Me I would do an engine flush several times and run some marvel m oil . If oil system very sludged it will keep blocking small screens and vct ports . Even if you do timing job the clean out will help . .
That's enough with the info at this point . You have way more info than we do
I would think you cleaned throttle body and maf .

 

 

The fuel pump driver module is on top of the frame cross member behind the gas tank.

 

I take it with those codes you used non genuine VCT solenoids. What about the cam phasers?

 

Yes you do not need to drop tire for fpdm its on the axle-- it may make it easier . But you do need to maint that spare tire/ tools should be under rear pass seat . And if you do need that tire, you better get it working now .
And just because you had a shop do plugs doesn't mean its done right . We like to think so but many on here will tell you they have been disappointed .
Well as complicated as life is going to get in the next 20 years patience and learning is going to be your future as I tell my grandkids. Just watched a guy rebuild a testla , thats a real learning experience that's one hell of a battery and lethal .
Perhaps a junk yard will have your jack and tools .
I have had to drop that tire with good clothes on and its a big reason to clean it every now and then not to mention airing it up . 'Both vcts should have been replaced ,new ones are better and screens and such get clogged . Some of us do a engine flush every other oil change ,plus I run 1 quart marvel m oil as slow cleaner .
.Best To clean throttle body and maf off the intake. Plus in reality I would clean injectors A vacuum leak is always possible when in there changing plugs ,old lines etc . That makes for a rough idle ,there are several ways to test for that/ one is a homemade smoke machine off you tube .05's had bad injectors so I replaced all mine at 130k ,and will again at 230k .They can kill an engine so I replace with new ,yes they are not cheap .
If your belt squealing it may be bad bearings in pulleys or a bad tensioner . You have a steel crank pulley so that's not the problem/ no rubber damper .

 

 

Error code P0174 is described as System Too Lean (Bank 2). This means there is incorrect ratio of air and fuel on the car's engine system, specifically on Bank 2 of the Cylinder. “Too Lean” means there is too much oxygen in the exhaust. bank 2 is drivers side .
P0303 Error Code P0303 is described as Misfire Detected, Cylinder number 3. This means the vehicle's computer has detected a misfire in the engine's cylinder number 3 which is passenger side third one back .
It determines a misfire if crank gets boost or not from that point of crank cycle . Not perfect .You can move no 3 plug, cop and injector to another cly . There may be other misfires but not as bad . Torque pro lets you see those building up per cyl.
Me I would run a vacuum smoke test with homemade smoke machine off you tube . Of course you cleaned maf and TB . You must have put a new fuel filter on it . Its not good to run fuel pump with low gas all the time as it cools pump . Torque pro will let you see fuel pressure on rail . Its a cheap diag tool for $5 ,you need android phone and cheap amazon bluetooth reader .
Yes this motor eats parts and it can be a bear to find problem .
Your 345 and 349 indicate the cam on bank 2 not where it is supposed to be ,perhaps the new vcts are jammed with dirt . You could pull bank 2 valve cover ,clean vct and inspect valve train . Dirty oil from vct drives cam phaser to position computer wants it . You can look at cam phaser to see if its distorted ,turn engine until 3 fingers are up ,middle finger timing mark . directly behind in line , the spring should not be distorted and finger plate should be parallel to cam gear . Of course if guides are broken then oil maybe getting blocked at oil pu screen . So low oil pressure can cause a lot of this . Basically if you drop oil pan and plastic in there then its time for a full timing job . I hate to bring bad news to Cesar but don't shoot the messenger . You are at the miles most fail, mine did before this .

 

 

Lot of possibilities...mine was doing the on / off rough running...turned out oil pump was losing pressure from time to time. Timing controlled by oil pressure. Engine finally gave up and blew apart. The engine was shaking so hard it actually broke both motor mounts.