No need to run synthetic if you only use is for short flush. What are you going to use to flush it. The shop that rebuld the head suggest me to use 1/2 quarts of marvel 500 miles before oil change.
I did not want to do that at that time because I heard some horror stories about the gunk clogging oil passage.

Did you try shut it down briefly and then restarting it. It works for me before and would get rid of the noise for a while.