Filling small CO2 bottles from large CO2 bottles?

[-CHRIS-]

So I have been filling my smaller 2.5 pound and 5 pound CO2 tanks off of a 20 pound liquid (dip tube tank.) It has been more or less trial and error, but I find if I freeze the destination tank it seems to work pretty darn well. I have run into a little issue recently, once the 20 pound tank has 7 pounds or less of CO2 in it, no matter what I do, I can only get 8-10oz of CO2 into it.

What am i doing wrong? Should I freeze the tank again to get it to accept more CO2? I thought about gently warming the 20 pound tank in my boil kettle to encourage more liquid to flow out?

Thanks,
Chris