Leveraging the growth of superconducting, epitaxial Al on a semiconducting InAs quantum well to fabricate gated Josephson junctions with highly transparent interfaces may prove vital for realizing near-term scalable quantum information processing on superconducting qubit circuits. Microwave performance on III-V/Al heterostructures, however, may be limited by threading dislocations in the bulk layers. For this reason, we investigate the growth of InAs/Al heterostructures strained to the underlying InP substrate. We grow thin films with AlAs and InGaAs insertion layers of various thicknesses between the InAs and Al regions. We study sample surface morphology and show that samples with a thin AlAs insertion layer have an improved surface morphology, with a lower root-mean-squared roughness by almost 0.5 nm. Through HAADF-STEM studies, we find that samples grown under suboptimal conditions lead to 10 nm large Al islands, while islanding is largely inhibited in samples with an insertion layer. We discuss implications of different materials systems for gate-voltage tunable Josephson junctions through ID Poisson simulations. We show that by improving the semiconductor-superconductor interface morphology, this materials platform is well suited for tunable quantum circuits.