Just drill some more holes, that's what I do, often doubling the number of holes, evenly spaced, because, for certain plants, sometimes the prepared thinner parts aren't enough, you're right, but if you have a drill, its fairly simple to make more. There is, though, the risk of the drill bit slipping and skidding because the material's thicker, so put some plaster (band aid fabric) or fabric like tape over the area you want to drill first, so that the bit bites properly. The only drawback is dependent on the type of plastic - if its fairly softish and a bit pliable, that's fine, but if it's sort of crisp and hard, that often cracks when you try to drill through. If its just a small crack, doesn't matter, its even better drainage, but there may be a risk of a large fracture.
Looking at your picture, I'd add 4 more holes, along the central strip, spaced apart, 2 either side of that darker circle in the middle and one towards both ends, between the two lighter circles. That should be plenty, but you can make more if you want.