Say that your end goal is to price an equity exotic derivative under both Heston and the local volatility models (Black Scholes model with vola dependent on strike and underlying level). Do the following approaches make sense?
Directly minimize distance between model derived (Heston/local vol) American option prices and observed market quotes.
Use SVI/SSVI and some interpolation/extrapolation to extend the BS-implied volatility surface that you obtain by inverting American option market quotes (using e.g. a CRR tree). Then derive Eurpean option prices from the surface using BS and minimize distance with the model derived European option prices.
