Recent experiments [Phys. Rev. B , 245123 (2024)] revealed striking inverse-current ($1/I$) quantum oscillations in quasi-one-dimensional charge-density-wave (CDW) insulators and proposed an intrinsic Floquet sideband mechanism arising from the sliding condensate. Here we develop the complete theoretical framework underlying this proposal. We provide an exact Floquet diagonalization of the uniformly sliding CDW problem, yielding split gap edges and a ladder of Floquet sidebands with explicit unitary transformation and spectral functions. Using this exact solution, we formulate weak-probe tunneling spectroscopy and demonstrate that the local Floquet spectrum naturally yields $1/I$ oscillations as successive sideband edges cross a fixed contact chemical potential. The measured period fixes $N_{eff}ϵ\simeq 4.80eV$, where $ϵ$ is the local contact-to-gap-edge offset. Combining this relation with the experimentally resolved low-temperature oscillations constrains the effective coherent channel count to be at most of order ${10}^3$, far below the geometric estimate $N_{geom}\sim 3\times {10}^4$, while $ϵ=10meV$ gives the representative value $N_{eff}\simeq 480$. This reduced coherent scale is naturally realized by a spatially nonuniform percolating network, but does not require $N_{eff}$ independent end-to-end wires. Furthermore, using a segmented multiterminal model, we show that inelastic phase-slip dephasing near the contacts explains the experimentally observed suppression of oscillation visibility on outer voltage probes. Finally, we contrast the persistent-current-driven multiterminal geometry with a homogeneous voltage-biased two-terminal reference calculation. Our results establish a nonequilibrium transport framework for the observed $1/I$ oscillations and identify an observability condition in which the Floquet spacing must exceed collective and quasiparticle broadening.