The lack of heat may be because there is poor secondary combustion due to weak draft. You can test this before committing to actually raising the chimney. Before it warms up too much outdoors, get a 4' section of inexpensive 6" round warm air duct. On a calm cold day remove the chimney cap and firmly insert the 6" round duct pipe into it, crimp down. Then go and start a fire and run the stove like that for a day or two. See if there is a notable improvement in heat output.
