Transition metal dichalcogenides (TMDs) constitute an intriguing platform for studying charge-ordered states including conventional and generalized Wigner crystals as well as Mott insulating states. In this work, we combine a phonon mode expansion of the electronic crystal vibrations with the Lindemann criterion to investigate the quantum and thermal stability of these strongly correlated phases in the exemplary materials of MoSe2 monolayers and twisted MoSe2-WSe2 heterostructures. We find that the moiré potential in heterobilayers acts as a harmonic trap, flattening the energy dispersion of phonon excitations and resulting in an order of magnitude larger melting temperatures compared to monolayer Wigner crystals. Furthermore, we explore the tunability of the correlated states with respect to dielectric environment and bilayer stacking. In particular, we show that the reduced screening in freestanding TMDs results in a tenfold increase in the melting temperature compared to hBN-encapsulated TMDs. Moreover, the deeper moiré potential in R-type stacked heterostructures makes generalized Wigner crystals more stable than in H-type stacking. Overall, our study provides important microscopic insights on the stability and tunability of charge-ordered states in TMD-based structures.