If you have decided that you need carb heat to deice the carb, you need lots, and you need it quickly, 'cause things are getting worse in the mean time. To get the most of the heat available from the engine, into the carb, after applying carb heat (and worrying more, 'cause now it's really stumbling), lean the mixture to achieve the most lean setting you can manage without making it run worse.
Hmmm. The logic and physics sort of makes sense but do you really want to add another variable (mixture setting) to the equation when dealing with a non-normal event? As the onset and clearing of carb ice is a dynamic process, the mixture ratio will be altering anyway without any input from the engine controls. Why further complicate the issue with a procedure that’s not in the POH?
IMHO, many icing events could be avoided/mitigated by a) a thorough understanding of the causes, b) regular checking and c) applying the clearance procedure in the correct way, i.e. giving it time to work.