Red Line 10w60 is already thicker than TWS and is more shear stable, meaning that you're running something HEAVIER than stock. You need to ignore the kinematic viscosity values and focus more on the oils' HTHS value as it is more indicative of the operational viscosity.
TWS has a virgin HTHS of around 5.2 and shears to around 4.5ish, then holds steady for the remainder of the change interval. Red Line 10w60 has a virgin of HTHS of 5.8 and probably only shears to the mid- or low-5s over its service life.
That means the Red Line is some 15% heavier than the already-heavy TWS. Personally, I would've just run the Red Line 5w40 (HTHS 4.4) -- it's basically the same weight in-operation as TWS.
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