To pass along some information, with pour in fuel additives, some of it ends up in the oil via blowby from combustion, which can cause problems for the oil.
With the fuel additive you are using, it could be negatively affecting the oil, increasing oil viscosity, (making it thicker), thus over time decreasing fuel economy, as you have noted.
Another part of the problem could be the oil itself, not staying in viscosity, becoming thicker and reducing fuel economy. What brand and type of oil are you using? Many of the, "synthetic oils", on the market today are really not synthetic motor oils at all, in the traditionally accepted definition of a synthetic oil. Buyer beware.
With either a 0W-20 or 5W-20 viscosity oil, (all else being equal), there will be no difference with the engine when it is hot, as both oils are a SAE 20 viscosity at hot engine temperatures. With cold engine starts the 0W-20 vs. the 5W-20 will flow faster to reach engine parts to provide lubrication and reduce wear. Using the incorrect oil viscosity can jeopardize the engine warranty.
There is no need or benefit in changing oil at the very expensive 3,000 mile drain pain interval anymore, (that goes back to the 1960's). Indeed, excessive oil changes can cause accelerated engine wear, reduce efficiency and reduce engine life. Even the greedy big oil industry doesn't recommend 3,000 mile intervals anymore. With a properly functioning quality oil and air filter, dirt is either filtered out or prevented from getting into the oil in the first place.
As an independent AMSOIL synthetic lubricants Dealer, my hundreds of customers and I been using up to 25,000 mile drain intervals for close to 30 years and have saved thousands of dollars in unneeded oil change costs, improved fuel economy and longer lasting engines that run, "like new", for a longer period of time.