The only "category" that should make a difference in calculating gain is whether the transactions were short-term or long-term. The overall gain (short-term plus long-term) should be the same whether you use average cost or specific lots, as long as your average cost calculation is correct.
If the sale of both lots (covered and non-covered) had the same character (i.e long-term or short-term), you can use the average cost for all the shares to calculate your gain.
Otherwise, you would have to calculate the average cost of the short-term holdings, whether covered or non-covered, and the average cost of the long-term holdings, whether covered or non-covered.
