From first hand experience, the lowest you can do this EE is on Round 6 because the key for the skull could be gotten on either rounds 5, 6 , or 7. With enough time management, and with a little patience and luck, you could complete the EE on Round 6 (I've done it onRound 7 because crawler round for me was on Round 6, but oh well, at least I did it on Solo too).