I think your analysis is correct.
_Dictyostelium_ generally means net-like pillar. _Dictyo_ references a net or mesh, and stele originates from the Greek _stēlē_ : to stand or pillar. However, as you point out, "stele" is also the word for the central vascular tissue in vascular plants. The stele can take on several different architectural arrangements, including a net, or dictyostele, in some ferns.
As I don't read German either, it's unclear to me if Brefeld was referencing the structure in ferns, or just describing _D. mucoroides_ on its own terms, perhaps envisioning the gathering of cells to form the stalk as being like a net. See, for example, this image of a _Dictyostelium_ aggregation.
!an aggregation of Dictyostelium forming a stalk
"Discoideum," as you note, means "disk-shaped," and Raper in his description references "expanded disklike bases" and "basal disks."