Welcome to the world of cascading changes of a tightly packaged design. Larger tires need more drive torque. One way to get this is to use the same motor with a different reducer that has a larger gear reduction ratio. Such a reducer, if one is even available, might not fit into the space of the existing gearmotor. Your idea of changing gears in the existing reducer is theoretically possible, but the practical reality is that it is almost always much more expensive than changing reducers.
Or you can increase the battery voltage, which will reduce motor life and could burn up the controller. Or you could fit a more powerful motor to the same reducer, which will shorten the life of the reducer if the controller will even deliver the necessary current. Or you could upgrade the gearmotor, controller, and battery. But that would not fit into the available space.
Have you looked into all terrain wheelchairs, sometimes referred to as rough terrain wheelchairs? There are a number of wheelchairs available that are specifically designed for unpaved terrain with steep slopes. Here is one that was randomly chosen from a search for all terrain wheelchairs:
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