Just to put this all in perspective:
The larger tire will result in ever so slight improvements in fuel economy - all other things being equal. The biggest problem is the "all other things" part.
Changing from P type tires to LT type tires is the wrong direction for F/E. LT tires are "work" tires and F/E isn't much of a consideration.
All Terrain tires will be worse than All Season tires. More mass.
There are tires with improved RR, but they frequently have sacrifices in treadwear or traction. That might be OK with you, but for many, it's not.
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