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A 205/45R16 tire would help, the 50-series tire is hair tall. Also varies from manufacturer to manufacturer. I had some Yokohamas in a 205/45R16 that rubbed the top of the fender liner and touched the rear trim by the mudflap on slight bumps. Swapped to a Kuhmo 204/45R16 - no more rubbing, unless I hit a big bump. Turns out - the Kuhmos were about 1/8" narrower than the Yokohamas
As for wheel offsets - Toyota spec'd wheels up to 7" in width and offsets from 38mm-45mm to fit without clearance issues. Of course, your mileage may vary.
Since you want to keep the tires - as mentioned above, probably have to adjust camber to tuck the wheel in and/or roll the fender lip + trim plastic bits to make the tire fit.
2002 Toyota Corolla S, 1.8L 1ZZ-FE VVT-i
2003 Toyota Matrix XRS, 1.8L 2ZZ-GE, VVTL-i (RIP)
2009 Toyota Matrix XRS, 2.4L 2AZ-FE VVT-i
2009 Toyota RAV4 Limited, 2.5L 2AR-FE Dual VVT-i