You may want to look at the literature on index
tracking; perhaps you find useful ideas there.
I would write and solve it as an optimisation
model. Since you seem most interested in the number of
assets that are required to closely replicate your
basket (i.e. the cardinality of the replicating
basket), you could solve the model for different
There are a few issues that need to be separated here.
Issue "zero" is whether your MC is able to correctly represent the dynamics you've chosen for your assets. If you implement your MC properly, by construction it should converge in distribution to the postulated dynamics. No bias there. Variance yes potentially, because of discretisation, but no ...
Another approach would have been to use some projection as in Pooley and Vetzal Convergence remedies for non-smooth payoffs in option pricing.
In your case, it may be a projection of the initial condition to the RBF space (I have read your paper, and it looks interesting). I wonder a bit how the two approaches compare.