Equivalent of SQL Not Exists in MDX (or finding another way to accomplish same result)
As you say it's hard to try out without your actual cube and it depends a bit on how your dimensions are layed out, but I think you can get there using the BOTTOMCOUNT function if you create  a measure on seq.


  BottomCount(Set_Expression, Count [,Numeric_Expression])  


Your set_expression could be a crossjoin between the dimensions you care about and you could create a dynamic set based on that expression.

Something along the lines of

WITH DYNAMIC SET LowestSeq AS
BottomCount({Part.Members * Customer.Members * Person.Members})
   , 1  
   , [Measures].[seq])


It would help if you published a small repro of your scenario as an XMLA script on pastebin or something. If your dsv is based on named queries producing the data we can easily create the same cube on our machine.