The only workarounds I can think of a
~ After you insert the row, trigger some code that rewrites the
formula. The insert and the rewrite could be combined into one
routine, and attached to a button on your sheet.
~ Before you insert the new row, convert the AVERAGE formula to a
static text string by replacing the equal sign in the formula with your
initials, or some random string of letters. After the insert, search
for the random string of letters and replace with the = sign.