Unstructured mesh CFD solvers with second order accurate spatial discretizations are flexible and ubiquitous in industry. Scale-resolving simulation techniques are viewed as the future for predictive fluid simulations, but standard technology is inefficient when repurposed for scale-resolving simulation. We show that greater efficiency can be gained using a stabilized-continuous-Galerkin finite element method with high-order basis functions on GPUs, using implicit time-stepping schemes. We explore trade-offs in the discretization and solver using a GPU implementation based on libCEED and PETSc, which enables portable performance from a single source code. We demonstrate accuracy, stability, and efficiency of our solver on turbulent compressible boundary layer flows.