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InAs quantum wells (QWs) grown on InP substrates are interesting for their applications in devices with high spin-orbit coupling (SOC) and their potential role in creating topologically nontrivial hybrid heterostructures. These QWs rely on InGaAs cladding layers and InAlAs barrier layers to confine electrons within a thin InAs well. The highest mobility QWs are limited by interfacial roughness scattering and alloy disorder scattering in the cladding and buffer layers. Increasing QW thickness has been shown to reduce the effect of both of these scattering mechanisms. However, for current state-of-the-art devices with As-based cladding and barrier layers, the critical thickness is limited to $\leq7$ nm. In this report, we demonstrate the use of strain compensation techniques in the In$_x$Ga$_{1-x}$As cladding layers, grown on In$_{0.81}$Al$_{0.19}$As barrier layers, to extend the critical thickness well beyond this limit. We induce tensile strain in the InGaAs cladding layers by reducing the In concentration from In$_{0.81}$Ga$_{0.19}$As to In$_{0.70}$Ga$_{0.30}$As and we observe changes in both the critical thickness of the well and the maximum achievable mobility. The peak electron mobility at 2 K is $1.16\times10^6$ cm$^2/$Vs, with a carrier density of $4.2\times10^{11}$ /cm$^2$. Additionally, we study the quantum lifetime and Rashba spin splitting in the highest mobility device as these parameters are critical to determine if these structures can be used in topologically nontrivial devices.