We study the total-mass density profiles of early-type galaxies (ETGs: ellipticals and lenticulars) with globular clusters (GCs) as kinematic tracers. The goal of this work is to probe the total mass distribution, parameterised with a double power-law profile, by constraining the parameters of the profile with a flexible modelling approach. To that end, we leverage the extended spatial distribution of GCs from the SLUGGS survey (⟨R_{GC, max}⟩∼8 R_e) in combination with discrete dynamical modelling. We use discrete Jeans anisotropic modelling in cylindrical coordinates to determine the velocity moments at the location of the GCs in our sample. Assuming a Gaussian line-of-sight velocity distribution (LOSVD) and a combination of informative and uninformative priors we use a Bayesian framework to determine the best-fit parameters of the total mass density profile and orbital properties of the GCs. We find that the choice of informative priors does not impact the enclosed mass and inner slope measurements. Additionally, the orbital properties (anisotropy and rotation of the dispersion-dominated GC systems) minimally impact the measurements of the inner slope and enclosed mass. A strong presence of dynamically-distinct subpopulations or low numbers of kinematic tracers can bias the results. Owing to the large spatial extent of the tracers our method is sensitive to the intrinsic inner slope of the total mass profile and we find ᾱ = −1.88 ± 0.01 for 12 galaxies with robust measurements. To compare our results with literature values we fit a single power-law profile to the resulting total mass density. In the radial range 0.1–4 R_e our measured slope has a value of ⟨γ_tot⟩= − 2.22 ± 0.14 and is in good agreement with the literature. Due to the increased flexibility in our modelling approach, our measurements exhibit larger uncertainties, thereby limiting our ability to constrain the intrinsic scatter σ_γ.