Estimate Partition Function from a simulation
What you're saying does make sense. You can, in fact directly estimate the partition function using nested sampling, with error bounds. See for example this paper http://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.174108 . In your case without PBC it's actually even simpler. Also check out Livia's blog here https://liviabpartay.wordpress.com/publications/