Can you not just discretize the target space? I mean, the compact boson is just a free field $\phi$ with the identification $\phi \sim \phi + \beta$. You could have a lattice with $L$ sites $x$ and at every site $\phi(x)$ can take values $0, \beta/N, \ldots, \beta$. You are truncating the spectrum of the theory, obviously: you only probe $\sim N$ vertex operators with low enough winding numbers and throw away the rest. The Hamiltonian would just be the kinetic term $(\partial_\mu \phi)^2$, and of course you need to take the identification $\beta \sim 0$ into account when computing its value. A nice feature is that this construction is obviously invariant under shifts $\phi \to \phi + \text{const}$.