Miss Fairfax (or is this Edward Fairfax Rochester speaking?) seems to be right, there does not appear to be a one-to-one translation. Where that is the case it often helps to go to descriptions of the object to which the word you are looking for refers.
Unfortunately Wikipedia's description of the famous Veit Stoss altar, which has one hell of a Gesprenge, does not mention it at all, though it is clearly visible in the photo provided (Wikipedia, s.v. Altar of Veit Stoss).
If you look under Ghent Altar you will find mention of "a very ornate carved outer frame and surround". This doesn't quite fit the emphatically vertical quality of a Gesprenge, however.
Under Isenheimer Altar there is a link to a well-informed article in which we find that "the sculpted base and crown of the altarpiece vanished“.
Hence my suggestion of "sculpted crown". Less clunky and more accessible to lay readers is "pinnacles", which, though an architectural term, gives a good idea of the himmelwärts strebende verticality of a Gesprenge.