Again, humbly suggesting and open for rebuffs, but here goes:
Sorry folks, but hierarchies really have only one task - to keep the processes more or less structured.
If you have an alternative way of structuring the processes and workflows you really have no need for hierarchies.
Thus the thingamy requires no hierarchy.
(Sure it can virtually represent one if you want to keep it for sentimental reasons.)
Sorry folks, positions and titles are a solely a part of the hierarchy - no hierarchy, no positions. Sorry.
(Sure the thingamy can virtually represent positions if you want to keep them for... ehh... whatever reasons. Ah yes, ladder-climbing as a motivator... as if that's the best one...)