Black hole low-mass X-ray binaries (LMXBs) are transient in nature, such that their luminosities and spectra evolve significantly over periods of weeks to months. Such changes are due to physical alterations to the structure of the accretion inflow and gaseous outflows. LMXBs spend most of their time in a hard state (wherein their X-ray spectra are power laws and thus dominated by higher energies), with order-of-magnitude variations in luminosity. A key issue in physically characterising this state is finding a way to dissect the components contributing to this power law emission: this has up to now proved challenging due to degeneracies in spectral modelling. Solving this issue of modelling degeneracy is vital in the broader context of understanding the physics of accretion around black holes, solar mass and supermassive alike---this is a key factor in the fields of active galactic nuclei feedback and supermassive black hole growth. It is also required for the determination of black hole spin via X-ray reflection modelling, since the results of such studies depend on the assumed geometry of the irradiator. In order to disentangle these components, one needs to invoke all the available spectral and timing information, and build a self-consistent physical picture. I will present work we have been doing on attempting to break modelling degeneracies by fitting a semi-analytical outflow-dominated model to broadband observations of GX 339-4 from radio to X-ray, tracking the evolution of key model parameters with the X-ray variability properties of the source. We jointly model the broadband spectra during states of similarity in variability properties, and find key best fit parameters hold indistinguishable values. I will discuss further work we are doing to advance X-ray reflection modelling by adding X-ray emission from the jet to current models.