Have you already drilled holes through the MDF? It sounds like you have. I drilled out all my holes in my panel before laminating and then used a router with a templateflush trim bit to finish the job through the button holes. If you have a plunge router you can plunge it right through the laminate (virtually no chance of chipping). If you have a fixed base router, just drill through the laminate from the under side with a drill bit just big enough to create a hole that the router bit will fit through (comfortably), and then use a router to finish the job.
Keep in mind, if you permanently mounted your carriage bolts under the laminate so the hardware would be invisible on top, you probably will need a flush-trim bit rather than a template bit, because the carriage bolts will get in the way of the router base on bottom. A flush trim bit has the bearing on the bottom of the bit, a pattern bit has the bearing between the cutting blade and the shank. If this is the case, I recommend masking the whole surface before you clean up your holes. You don't want to scratch that surface while putting the finishing touches on it.