Basically you have two options:
1) Make a dashboard from 6 pieces (1-row / 3-Marks each).
2) UNION ALL your datasource table 6 times
and use [Table Name] as a Dimension in Rows
(instead of [Measure Names]) together with
a single calculated Measure for sorting/ranking.
If a third option exists, i'm afraid i'm not aware of it (yet).
Thanks Yuriy Fal,
I actually ended up going with the first option. It did make the calculations A LOT slower on Tableau Server, but at least it worked.