I would not use a bigger antenna since your signals are already strong.
Actually, a "bigger", "stronger", "longer-range", etc antenna would provide a significant opportunity for improved reception.
Such antennas are going to be more directional at the expense of increased physical size (length and # of elements, usually). This will do several good things simultaneously, like improve the signal power of the desired signals, reject undesired signals (noise) from other directions, and improve the ratio between the desired signal and other noise sources. There is no danger of overloading the system from an antenna alone since the signal powers in the forecast do not take into account the transmitting antenna tilt or its vertical (elevation) pattern. Most likely, the main lobe of the transmitting antennas' signals is still well overhead in this location. Installing such an antenna so it's shielded from reflections from the interstate would help reduce those dynamic multipath problems.
It has been my observation and experience when using TVFool's simulator, that, for locations immediately on the back side of a hill, the estimates are usually way too optimistic.