Infrared carbon stars without visible counterparts are generally known as extreme carbon stars. We have selected a subset of these stars with absorption features in the 10-13 µm range, which has been tentatively attributed to silicon carbide (SiC). We add three new objects meeting these criterion to the seven previously known, bringing our total sample to ten sources. We also present the result of radiative transfer modeling for these stars, comparing these results to those of previous studies. In order to constrain model parameters, we use published mass-loss rates, expansion velocities and theoretical dust condensation models to determine the dust condensation temperature. These show that the inner dust temperatures of the dust shells for these sources are significantly higher than previously assumed. This also implies that the dominant dust species should be graphite instead of amorphous carbon. In combination with the higher condensation temperature we show that this results in a much higher acceleration of the dust grains than would be expected from previous work. Our model results suggest that the very optically thick stage of evolution does not coincide with the timescales for the superwind, but rather, that this is a very short-lived phase. Additionally, we compare model and observational parameters in an attempt to find any correlations. Finally, we show that the spectrum of one source, IRAS 17534−3030, strongly implies that the 10-13 µm feature is due to a solid state rather than a molecular species.