Hmm... What you suggest seems like the most obvious way. Seems a bit of a waste of coolant though.
As bit of a low-tech alternative, have you tried connecting up some pipes and blowing hard to see if it will expel the water?! Depends how it's all connected up internally though I suppose. May do nothing at all.
The piping inside the chiller is quite large but if I lay it on it's side I may be able to shift it by connecting up some pipes and blowing.
Thanks