Could I buy a 16 gallon keg and only fill it with 10 gallons of beer and just fill all the headspace with co2? Will this cause the beer to absorb too much and be too carbonated?
Yes you can do that. As long as you have a pressure regulator the head space does not influence how much your beer will be carbonated. Remember that CO2 dissolution in beer mainly depends on pressure and temperature, so consult a table like this this and see what's best for your setup. Hope it helps.