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There's no way to reference the current dimension value in set analysis. In fact, the set is only calculated once, and for the entire chart.
Attached is what I consider to be a bad solution, but that may be better than no solution. Make a date island - the same dates, but disconnected from your data model. Use THAT date as the dimension. Then use an expression like sum(if("Date"<="Other Date",Value)). The big problem here is inefficiency. No problem for a sample like this, but could get ugly for a large data set. Another problem is usability, where selections in the chart aren't selecting the real data field, and vice versa. In the attached example, I try to address this a bit through conditional set analysis in the chart:
if(getselectedcount("Date")
,sum({<"Other Date"="Date","Date"=>} if("Date"<="Other Date","Value"))
,sum( if("Date"<="Other Date","Value")))
But selecting dates in the chart still won't affect OTHER charts, and things can still get a little funny. Another approach would be to ONLY let them select "Other Date", and do ALL of your connections via set analysis or IFs, but that can be a big maintenance headache.
Unfortunately, I don't have a better solution. I've tried half-heartedly in the past, and not succeeded. I say half-heartedly because I've never needed to do this for my own applications. It's just the kind of thing that should have a clean, simple and efficient solution, so I occasionally poke at it.
Hopefully someone else knows a good solution. I'd love to see it, even if it makes me feel stupid when I see how simple it is. 
