Context. Solar analogs are stars whose fundamental properties closely match those of the Sun and, as such, they serve as useful laboratories for tests of stellar structure and evolution, particularly in the context of the upcoming PLATO mission. Aims. Our study is focussed on six seismic solar analogs observed by Kepler and K2, which have been characterised in detail in a former analysis. We investigate the impact of the model physical ingredients on these six targets to evaluate how well we can satisfy the PLATO precision requirements for stellar parameters with the data quality that is currently available. Methods. We used the stellar mass, age, and chemical composition obtained with the Forward and Inverse COmbination (FICO) procedure, based on OPAL opacities and a combination of NACRE II and Solar Fusion II (SFII) nuclear reaction rates, as our reference values. The efficiency of macroscopic transport was calibrated on lithium abundances derived from the analysis of HERMES spectra. Next, we carried out extensive tests of the physical ingredients with the help of a Levenberg-Marquardt local minimisation method, using both classical (luminosity, mean density, metallicity, and effective temperature) and seismic constraints (frequency separation ratios). In particular, we investigated the impact induced by the use of OPLIB opacities and SFIII nuclear reaction rates on the stellar fundamental properties, as well as the use of various seismic constraints. Results. We quantified the potential differences that changes in the modelling input physics might lead to and compared their extent with the requirements expected for the PLATO mission (15% in mass, 2% in radius, and 10% in age), providing crucial constraints on the accuracy and robustness with respect to systematics of the determination of fundamental properties for PLATO. For our sample of solar analogs, we were able to accurately retrieve the stellar masses within 2.5%. As for the stellar ages, we quantified the systematics of the order of 10--14% at most, but there are also very promising cases for which deviations remain within 4% depending on the stars and constraints considered.