I think you can additionally do a variance reduction thing on your monte carlo simulations. For example I think you can compute an appropriate weighted sum of two call options, each on just one of the stocks, which hopefully can be done analytically. Then when you do simulations, you tweak your realized input for the basket call. You can also create a fictitious asset created from the other two and price a call on that one analytically to get more variance reduction. This is probably done in a lot of textbooks, but I've seen it in Cont and Tankov.