The compliance and other nonlinear dynamics of large-scale soft robots makes effective control difficult. This is especially true when working with unknown payloads or when the system dynamics change over time which is likely to happen for soft robots. In this paper, we present a novel method of coupling model reference adaptive control (MRAC) with model predictive control (MPC) for platforms with antagonistic pneumatic actuators. We demonstrate its utility on a fully inflatable, six degree-of-freedom pneumatically actuated soft robot manipulator that is over two meters long. Specifically, we compare control performance with no integral controller, with an integral controller, and with MRAC when running a nominal model predictive controller with significant weight attached to the end effector.