Ask yourself is there one reason other than EPA/CAFE standards Ford would recommend a 20W in your Coyote? If you are unable to find a reason 30W is your answer.
My choice would be Quaker State 5W-40 for a good balance of value and protection at $22 5/qts delivered.
Drop the rear diff fluid at 2k as well. Grab a different rear diff cover that will allow for easy drains in the future without removing the cover. Diff cover and Better gasket Double check me on your application but I would do these.
For engine oil, a quality 5W-30 with 5k intervals should do...
Because this started right after the wheel/tire replacement I would look at the hub surfaces as I mentioned prior. You could check for wheel run out on the truck and if so that could be the issue. This will show a surface to surface issue while installed.
Raise truck and secure a plastic pry...
Yet they will also install start/stop equipment or DOD/AFM systems which reduce reliability, increase manufacturings costs and increase warranty costs to help maintain CAFE/EPA compliance.
My opinion is the recommended oil is a part of compliance, not what GM would ultimately recommend.