Extending multiple surfaces to meet and join each other

I started with a large polysrf composed mainly on triangles meeting at different angles, exploded it and offset the individual srfs, now I need to create a new polysrf by extending and joining all of these srfs together.  Essentially it needs to be the same polysrf but larger by the offset distance.

The original joined polysrf will not offset properly, I've tried JoinEdge, ConnectSrf, MatchSrf, ExtendSrf, as well as everything else in my bag of tricks.

The offset srf represents the material thickness that this piece will be built out of so it is crucially important that it is accurate since ther will be an additional layer of pieces on top of it.

Top pic shows the overall polysrf, lower one shows an intersection of six triangles with their offsets in green/blue.  How do I join these offsets into a new polysrf?



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