Transmission fluids do not have any extra chemicals to clean an engine. That is an ol' wives tale. Since ATF doesn't have to deal with combustion byproducts, its has a lower dosage of detergents and dispersants when compared to cheap motor oil.
The 2gr in my '08 recommends 5w20 for non tow package and 5w30 for tow package. So, explain why the engine, when equipped with an oil cooler/heater, needs a thicker oil? I do miss the 5k mile recommended intervals. I've seen nothing but problems from automakers recommending longer intervals. My 2gr in the '11 is a different vehicle and Toyota recommends 5w30 only but some claim 5w20 backspec'd. The 2gr in the '16 recommends 0w20. And, there is no difference in these engines. The 08 and 11 recommend 5000 mile changes. The '16 recommends 10000 mile changes. In foreign markets, the 2gr can take 10w30, 15w40, 20w50..... There is no difference in the engines. So, weather permitting, you can use whatever grade you want.
And, there is no issue with thicker oil flowing thru the screens. Your 0w20 COLD is thicker than a 20w50 HOT.
No need for the Toyota oil filter and never has been... conventional cellulose media is slowing heading into obsolescence, about 30 years too late.
Can mask some noises with thicker oils. I run the gauntlet of high HTHS 5w30's, 0w40's 5w40's, 10w40's... in mine. Just consider weather/temps and don't go overboard. And, as always, run synthetic oil.
I only recommend synthetic oil. There is no 'magical' brand of oil. So, use whatever brands you want and there is no issue with alternating among the brands.
Conventional oil is slowly heading into obsolescence.... about 30 years too late.
If you think your engine is dirty, then shorten your oil change interval considerably, use quality current spec oils and synthetic media filters.
Clean your VVT screens. If they are dirty, then your maintenance is lacking. Pull a rocker cover and inspect for sludge. If there is any sludge, then your maintenance is lacking. You reap what you sow with your noisy dirty engine.