'Jack sang in a park this morning as he did two days ago.' -- he sang on the 29th and 27th.
'Jack sang in a park this morning, as he did the two previous days.' -- he sang on the 29th, 28th and 27th. You could also express this as 'as he did on the two days before', Jobb.
'Better'? I would probably use the past perfect here if I were writing a thesis, a careful formal letter, or a piece of literature (and I think I would be overconservative in doing so). What would I say if I were talking about my wierd friend, Jack? 'Jack sang in the park again this morning-- he did it yesterday too-- and the day before!' Or something like that.