A g-tuple of disjoint, linearly independent circles in a Riemann surface Σ of genus g determines a ‘Heegaard torus’ in its g-fold symmetric product. Changing the circles by a handleslide produces a new torus. It is proved that, for symplectic forms with certain properties, these two tori are Hamiltonian-isotopic Lagrangian submanifolds. This provides an alternative route to the handleslide-invariance of Ozsváth–Szabó’s Heegaard Floer homology.