Lieber Peter,
Du scheinst recht mit Deiner Vermutung zu bekommen. Anscheinend wusste Jacques Fournier schon von Deinem Tip! (Die Welt ist klein)
Diese E-mail habe ich gerade von ihm erhalten:

Dear Christiane,
thanks for your message.
I think your fungus is not a Xylaria, but better a Podosordaria, as suggested by Peter Welt. It is rather easy to obtain such rhizomorphs when you incubate rabbit dung, the white mycelium invades all the box and yields these stout rhizomorphs within a few weeks. I obtained them several times (see attached photo) but the white tips remain sterile and no anamoprh is produced. I recently came across a paper by Webster and Weber, Mycologist (if you search on Google you will easily find the reference) where they report the same thing and observed that when the colony is buried in the ground, the rhizomorphs keep on developing and fertile stromata of Podosordaria tulasnei can occur. I took that from the abstract but I failed to get the full paper.
I just buried in my garden such a colony one month ago and I am looking forward to seeing what happens! I suggest you do the same, and let's kep in touch to see who will get something like photo2. Podosordaria tulasnei is a common dweller of rabbit pellets, if it does not work this time, we'll be hopefully more lucky another time. It is very rarely recorded because it is very difficult to spot in natural conditions, I guess it should be easier that way.
Best wishes,
Jacques

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Jacques Fournier
Ich werde seinen Rat befolgen, mal sehen was dabei rum kommt.

Liebe Grüsse
Christiane