The Shaped Pupil Coronagraph (SPC) is a high-contrast imaging system pioneered at Princeton for detection of extra-solar earthlike planets. It is designed to achieve 10^-10 contrast at an inner working angle of 4λ/D in broadband light. A critical requirement in attaining this contrast level in practice is the ability to control wavefront phase and amplitude aberrations to at least λ/10⁴ in rms phase and 1/1000 rms amplitude, respectively. Furthermore, this has to be maintained over a large spectral band. The High Contrast Imaging Testbed (HCIT) at the Jet Propulsion Lab (JPL) is a state-of-the-art facility for studying such high contrast imaging systems and wavefront control methods. It consists of a vacuum chamber containing a configurable coronagraph setup with a Xinetics deformable mirror. Previously, we demonstrated 4x10^-8 contrast with the SPC at HCIT in 10% broadband light. The limiting factors were subsequently identified as (1) manufacturing defects due to minimal feature size constraints on our shaped pupil masks and (2) the inefficiency of the wavefront correction algorithm we used (classical speckle nulling) to correct for these defects. In this paper, we demonstrate the solutions to both of these problems. In particular, we present a method to design masks with practical minimal feature sizes and show new manufactured masks with few defects. These masks were installed at HCIT and tested using more sophisticated wavefront control algorithms based on energy minimization of light in the dark zone. We present the results of these experiments, notably a record 2.4×10^-9 contrast in 10% broadband light.