We present an analysis of instrument performance using new observations taken with the Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS) instrument and the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system. In a correlation analysis of our datasets (which use the broadband mode covering J through K band in a single spectrum), we find that chromaticity in the SCExAO/CHARIS system is generally worse than temporal stability. We also develop a point spread function (PSF) subtraction pipeline optimized for the CHARIS broadband mode, including a forward modelling-based exoplanet algorithmic throughput correction scheme. We then present contrast curves using this newly developed pipeline. An analogous subtraction of the same datasets using only the H band slices yields the same final contrasts as the full JHK sequences; this result is consistent with our chromaticity analysis, illustrating that PSF subtraction using spectral differential imaging (SDI) in this broadband mode is generally not more effective than SDI in the individual J, H, or K bands. In the future, the data processing framework and analysis developed in this paper will be important to consider for additional SCExAO/CHARIS broadband observations and other ExAO instruments which plan to implement a similar integral field spectrograph broadband mode.