Toyota generally uses what I call a "Primary" and "Backup" misfire detection scheme.
The "Primary" detector monitors the primary winding current of each spark coil, for each and every spark event. If this current is too high or too low, a fault code is set (301, 302, etc) that identifies the specific coil or coils with the out-of-limits current. If the current is "way" out of limits, the fuel will be cut to that cylinder, to protect the catalytic converter, creating a noticable miss or skip at low RPMs.
"Backup" detection is accomplished by checking for a slight increase in instantaneous engine RPM immediately after each spark plug fires. When this increase is not detected, a code is set (such as 353) that is not cylinder-specific, particularly so when the problem is irregular and/or random.
I've interpreted your message to mean you initially had a "Primary" fault code implicating 1 or 2 spark coils, which you replaced, and now you have a "Backup" fault code.
My best guess is one of the following:
The weak spark coil (or coils) caused the related spark plugs to become fouled.
You or your mechanic did not apply dielectric grease to the new spark coil boots, and some arcing to the engine is occurring in the spark plug wells. This would be more noticeable when the humidity is high and the engine is under load.
You can test both theories by removing and inspecting the spark plugs under the new coils, and applying a film of high-temperature dielectric grease where the end of the boot contacts the body of the plug.
Source of this information is the Toyota ingition diagnostics training manual. I am not a mechanic, but design some of the electroniuc components used within spark coils.