After thousands of hours on the lesson tee, this is probably the most common "Self Diagnosis" that I hear from new students. I completely understand that you are contacting the ball either thin or heavy, The fault is NOT a premature lifting of your head or the inability to "Keep your eye on the ball". 
Your friend's good intentioned fix - "Keep your head down!", is one of the most detrimental to solid ball striking. 
Pictured are two professional golfers who have posted tournament rounds in the 50's. Observe that neither are keeping their head's down or looking at the ball, pre-impact. I could add many other examples as well.
The problem is your swing radius is inconsistent. There are a myriad of reasons why this is occurring. Like finger prints, we all have our individual tendencies and patterns. End the guessing and frustration. Get on a Plan to Better Golf! We will assess your swing and assign drills for your improvement.

" Dear Mr. Howes, Thanks for your input on the internet, particularly your article on lag.  I used to live in Santa Cruz, California, in the 80's, was something of a golf nut, and one day with friends traveled down to Carmel and attended a clinic conducted by Ben Doyle in which he talked about Sustain the Lag, but I never did get what he was saying.  It seemed way over my head.  Many, many years later I read your GolfWRX article and finally got it.  Thanks again for the article, you are very much appreciated! " - B.H.
 "To View Article Click Pictures for Link"

On The Course

Impact: Training

Club Head Lag

Driving Help

Stressing the Shaft

Slice Help Part 1

Slice Help Part 2

Slice Help Part 3

Bent Left Arm