Fill the bottles. It's counter-intuitive, but that extra headspace will a lot more pressure or foaming. I've experienced this and wondered why.
I have a theory...
When you properly fill the bottles, your CO2 fills the headspace, then is reabsorbed at the proper levels to create an equilibrium, with just a little surface area in the neck of the bottle.
If you underfill, more of the CO2 stays in the large headspace, and reaches a lower equilibrium volume in the beer, with a larger percentage of the pressure coming from the gas in the bottle, versus the glass surrounding the beer.
When you pop the top, that CO2 evacuates quickly to equilibrium with the atmosphere, leaving a massive negative pressure on the beer, causing it to foam more quickly.
A smaller headspace means that most of the pressure on the beer is coming from the bottle surrounding it, and has very little surface area in contact with the now evacuated headspace, so the pressure drop agitates far less beer.
Btw, that first part also suggest that overfilling will create too much pressure during the early stages- causing greater upwards and downwards pressure (the ring of the neck is the strongest part of the bottle, so it has little give). This would cause either the top to pop (requiring breakages of the lip of the bottle, rather sturdy, or releasing the crimped steel of the cap), or more often, causing the relatively thin transition of the bottom of the bottle to the side wall to give out, as the beer is pushed down against it. If the bottle holds, you're fine, but any fault will show that might normally have survived the rated carbonation level.