I think he still would have given Harry the memory. They where running out of time and the amount that was in his memory probably would have lasted about 10-15 minutes. Even snape wouldntve been able to explain all of that in as much detail as he could and still expect Harry to believe him. He would have needed harry to have seen the full story. Like the saying goes "you would have had to be there to believe it". I think that this is exactly the time to use that phrase. Harry would need to see everything to believe how much snape felt about lily.