The issue I have with these approaches is that they use the unconditional distribution to eliminate the latent volatility. However, when the volatility process has very weak mean reversion one would need a very long and clean sample to make robust parameter identification from the unconditional density. They just throw away all the information from the transition dynamics.
My preference is a filtering approach. There have been some older papers that did that, google for Heston together with Ghysels, Gallant, Renault, Chernov, Tauchen, Pan, Bates, Shephard, MCMC, unscented Kalman filter and you will get some references. It is still ugly, since volatility is unobserved, but at least you are looking at conditional transitions rather than the stationary distribution. Even better, you can implied vols and perform joint estimation. Some of the references above do that too.