Why do higher-mass isotopes have higher melting and boiling points than lower-mass isotopes?
As you already mention in your question, melting and boiling of a substance is related to the inter-particle forces. You also correctly assumed that the same number of electrons results in identical (electronic) bonding properties, which basically is a different formulation of the Born-Oppenheimer Approximation (as in the BOA the nuclear mass is assumed to be infinite, different isotopes should have the same electronic structure). 

So what is the difference then? 

Well, it's in the vibration between the different particles. Consider a number of (neutral) particles in a certain phase (it can be solid, liquid or gas) at a certain distance with respect to each other. Because of dispersion forces between the particles, they interact and to a first approximation, every particle experiences a harmonic force $F(x)=-k(x-x_e)$. The magnitude of this force depends on the distance between the particles and on the electronic structure of the particles and in principle not on the mass. However, as you might know, a harmonic force in quantum mechanics results in quantized energy levels given by

$$
E_v=h\nu_e(v+\frac{1}{2}),
$$
where $E_v$ is the vibrational energy of the $v$th level and $h$ is Planck's constant. What is important to realize is that the energy of the lowest state is not equal to zero but has a value of $h\nu_e/2$, which is referred to as the zero point energy. Of course the potential is not really harmonic but rather anharmonic so that at a certain distance between the particles the force becomes negligible and the particles dissociate (or melt or evaporate). The lower the zero point energy, the larger the binding energy. The constant $\nu_e$ is given by $\nu_e=\frac{1}{2\pi}\sqrt\frac{k}{\mu}$, where $k$ is the harmonic force constant and $\mu$ is the reduced mass. The constant $k$ is the same for the different isotopes as it depends on the electronic potential between the particles but the reduced mass is of course different for the different isotopes. As you can see from the definition of $\nu_e$, the heavier species have a smaller zero point energy and thus a larger binding energy and will require higher temperatures to melt and boil.