As said already, but I'll try to summarize:
Gearbox reducer ratings are primarily based on torque at the output shaft. Not all customers prefer to calculate this, so many manufacturers provide instead a HP rating chart at various common speeds. If you do the math, you'll see they are usually about the same torque for any given ratio/configuration. These ratings should cover the limits of the gearbox fracturing the teeth (sudden) or tooth surface fatigue (gradual) failures, whichever is lower. As you have proposed to change the motor, the torque will increase and the gearbox rating will go down, leading to either a greater risk of failure when overloaded or loss of overall lifespan.
In most cases, the rating is not as much as the peak load encountered in startup or upset conditions. Therefore rating is not enough for most cases. We call this extra margin service factor. Service factor = gearbox rating / actual load. 1.5 to 2.0 is popular for many industrial applications with well-understood loading.
The thermal rating is another limit that can come into play, but it tends to follow HP and speed. Given the same HP and lower speed motor you mentioned, the box should run cooler. If you are buying a drive where thermal rating might be a factor, try to understand how much temperature rise is expected with the thermal rating. Some drives run much hotter than you would expect.
The bearing life will change also. While the bearings will rotate through fewer load cycles per minute, the load on the bearings follows torque, which is increased. Of the two opposing factors you should see a net loss of bearing life as a result of the higher load and less optimal lubrication conditions.
Depending on your application, the gearboxes you consider may have some/all/none of this in their engineering tables. (For example, for slow-speed drives thermal may never be a practical problem and therefore omitted) It would concern me greatly if your gearbox supplier is not familiar with all of this.
Up-sizing the gearbox was a wise choice. It insures your service factor is maintained.
Hope this helps.
David