Rendering with higher resolution would not solve your problem. If your final display size is 1920x1080 for example, rendering it at 4k will take a lot longer, but since your final display size is 1920x1080, all those extra pixels are lost when it is scaled or sampled back down the needed size. Make sense?
If you can't change the main lighting, then as noted above, randomize the material and add a tiny bit of reflection. In real life, there are many times you cannot see certain details based on the angle. Photographers cheat all the time by adding a subtle light just to catch certain edges or add reflections. So you're not changing your lighting, just adding a cheat code.
Also, make sure your edges are not perfectly sharp. Can't quite tell from the renders, but they look like they need a little rounding or beveling. That will also help catch light.
