Most models identify the X-ray bright North Polar Spur (NPS) with a hot interstellar (IS) bubble in the Sco-Cen star-forming region at $simeq$130 pc. An opposite view considers the NPS as a distant structure associated with Galactic nuclear outflows. Constraints on the NPS distance can be obtained by comparing the foreground IS gas column inferred from X-ray absorption to the distribution of gas and dust along the line of sight. Absorbing columns towards shadowing molecular clouds simultaneously constrain the CO-H$_{2}$ conversion factor. We derived the columns of X-ray absorbing matter NH(abs) from spectral fitting of dedicated XMM-Newton observations towards the NPS southern terminus (l=29{deg}, b=+5 to +11{deg}). The IS matter distribution was obtained from absorption lines in stellar spectra, 3D dust maps and emission data, including high spatial resolution CO measurements recorded for this purpose. NH(abs) varies from $simeq$ 4.3 to $simeq$ 1.3 x 10$^{21}$ cm$^{-2}$ along the 19 fields. Relationships between X-ray brightness, absorbing column and hardness ratio demonstrate a brightness decrease with latitude governed by increasing absorption. The comparison with absorption data, local and large-scale dust maps rules out a NPS near side closer than 300 pc. The correlation between NH(abs) and the reddening increases with the sightline length from 300 pc to 4 kpc and is the tightest with Planck $tau_{353}$-based reddening, suggesting a much larger distance. N(H)/E(B-V) $simeq$ 4.1 x 10$^{21}$ cm$^{-2}$ mag$^{-1}$. NH(abs) absolute values are compatible with HI-CO clouds at -5 $leq$ V(LSR) $leq$ +25 to +45 km s$^{-1}$ and a NPS potentially far beyond the Local Arm. A molecular cloud shadow at b=+9deg constrains X$_{CO}$ to $leq$ 1.0 x 10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s. The average X$_{CO}$ is $leq$ 0.75 x 10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s.
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