Opacity is a critical parameter in the simulation of radiation transport in systems such as inertial confinement fusion capsules and stars. The resolution of current disagreements between solar models and helioseismological observations would benefit from experimental validation of theoretical opacity models. Short pulse lasers can be used to heat targets to higher temperatures and densities than long pulse lasers and pulsed power machines, thus potentially enabling access to x-ray emission spectra at conditions relevant to the radiative zone of the sun. The radiation-hydrodynamic code HYDRA is used to investigate the effects of separately modifying laser energy, laser pulse length, and target dimensions on the plasma conditions, x-ray emission, and inferred opacity of a buried layer iron target. The plasma conditions are controlled by the laser energy and tamper thickness while the accuracy of the opacity inference is sensitive to tamper emission and optical depth effects. As an extension of the single parameter studies, a process using Lawrence Livermore National Laboratory's Uncertainty Quantification Pipeline has been developed to simultaneously optimize laser and target parameters to meet a variety of design cases. Two sets of design cases were explored: a set focused on conditions relevant to the radiative zone of the sun (electron temperatures of 200 to 400 eV and densities greater than 1/10 of solid density) and a set focused on reaching temperatures consistent with deep within the radiative zone of the sun (500 to 1000 eV) at a fixed density. Optimized designs of a buried layer iron target were found. It was determined that the appropriate dopant, for inferring plasma conditions, depends on the temperature reached: magnesium for up to 300 eV, aluminum for 300 to 500 eV, and sulfur for 500 to 1000 eV. The optimal laser energy and buried layer thickness increase with goal temperature. The accuracy of the opacity inference is limited to between 12 % and 26 %, depending on the design. Overall, short pulse laser heated iron experiments reaching stellar-relevant conditions have been designed with consideration of minimizing tamper emission and optical depth effects while meeting plasma condition and x-ray emission goals.