  The singlet dynamics which plays a major role in the physics of the spin-1/2
Quantum Heisenberg Antiferromagnet (QHAF) on the Kagome lattice can be
approximately described by projecting onto the nearest-neighbor valence bond
(NNVB) singlet subspace. We re-visit here the effective Quantum Dimer Model
which originates from the latter NNVB-projected Heisenberg model via a
non-perturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact
diagonalisation on a 108-site cluster supplemented by a careful symmetry
analysis, it is shown that a previously-found 36-site Valence Bond Crystal
(VBC) in fact competes with a new type of 12-site "{\it resonating-columnar}"
VBC. The exceptionally large degeneracy of the GS multiplets (144 on our
108-site cluster) might reflect the proximity of the Z_2 dimer liquid.
Interestingly, these two VBC "emerge" in {\it different topological sectors}.
Implications for the interpretation of numerical results on the QHAF are
outlined.
