  Webs yield an especially important realization of certain Specht modules,
irreducible representations of symmetric groups, as they provide a pictorial
basis with a convenient diagrammatic calculus. In recent work, the last three
authors associated polynomials to noncrossing partitions without singleton
blocks, so that the corresponding polynomials form a web basis of the pennant
Specht module $S^{(d,d,1^{n-2d})}$. These polynomials were interpreted as
global sections of a line bundle on a 2-step partial flag variety.
  Here, we both simplify and extend this construction. On the one hand, we show
that these polynomials can alternatively be situated in the homogeneous
coordinate ring of a Grassmannian, instead of a 2-step partial flag variety,
and can be realized as tensor invariants of classical (but highly nonplanar)
tensor diagrams. On the other hand, we extend these ideas from the pennant
Specht module $S^{(d,d,1^{n-2d})}$ to more general flamingo Specht modules
$S^{(d^r,1^{n-rd})}$. In the hook case $r=1$, we obtain a spanning set that can
be restricted to a basis in various ways. In the case $r>2$, we obtain a basis
of a well-behaved subspace of $S^{(d^r,1^{n-rd})}$, but not of the entire
module.
