For an 8 to 10 hour cook I tend to use an average of 1 chunk per hour on long cooks. Never have had anything get overly smoky. Some types of wood may be much stronger than apple or hickory and I might not get away with using so much.
Mesquite would be one of those woods that you don't want to add a ton of because it is so strong. That might get the overly smoky flavor you are describing.
I don't use chunks, but I would think if you burn 1 chunk per hour, it wouldn't get too smoky, but if you have 7 chunks in there & they all burn & smoke at one time, any species could get to taste too smoky.
Bear
Your chunks are on the smaller side so you should be fine. I agree with Ray and bury them into the charcoal. For fish and poultry I like fruit woods and for beef and pork mostly hickory.
Chris