You may be right about the reason for that Gamma-Gerät surviving. Either way, it was a WW1 weapon which escaped the Allies.
Incidentally, in 'German Heavy Mortars', Joachim Engelmann displays a photo which purports to be of a Dicke Bertha exhibited in the Deutsches Museum in Munich.
It's actually a full-size wooden model built by Emil Cherubin in 1932. You can see more photos in a piece I contributed to Landships (bottom of the page):
There's a charming little book about Cherubin, 'Die "Dicke Berta" aus Vluynbusch' by Raimund Lorenz. Packed with photos, it also shows that Cherubin built 1/4 scale wooden models of both the Dicke Bertha and the Paris Gun!