We present SOFIA/HAWC+ continuum polarisation data on the magnetic fields threading 17 pc-scale massive molecular clumps at the western end of the $η$ Car GMC (Region 9 of CHaMP, representing all stages of star formation from pre-stellar to dispersing via feedback), revealing important details about the field morphology and role in the gas structures of this clump sample. We performed Davis-Chandrasekhar-Fermi and Histogram of Relative Orientation analyses tracing column densities 25.0 $<$ log($N$/m$^{-2}$) $<$ 27.2. With HRO, magnetic fields change from mostly parallel to column density structures to mostly perpendicular at a threshold $N_{\rm crit}$ = (3.7$\pm$0.6)$\times$10$^{26}$ m$^{-2}$, indicating that gravitational forces exceed magnetic forces above this value. The same analysis in 10 individual clumps gives similar results, with the same clear trend in field alignments and a threshold $N_{\rm crit}$ = (1.9$^{+1.5}_{-0.8}$)$\times$10$^{26}$ m$^{-2}$. In the other 7 clumps, the alignment trend with $N$ is much flatter or even reversed, inconsistent with the usual HRO pattern. Instead, these clumps' fields reflect external environmental forces, such as from the nearby HII region NGC 3324. DCF analysis reveals field strengths somewhat higher than typical of nearby clouds, with the $Bn$ data lying mostly above the Crutcher (2012) relation. The mass:flux ratio $λ$ across all clumps has a gaussian distribution, with log$λ_{\rm DCF}$ = -0.75$\pm$0.45 (mean$\pmσ$): only small areas are dominated by gravity. However, a significant trend of rising log$λ$ with falling $T_{\rm dust}$ parallels Pitts et al's (2019) result: $T_{\rm dust}$ falls as $N_{\rm H_2}$ rises towards clump centres. Thus, in this massive clump sample, magnetic fields provide enough support against gravity to explain their overall low star formation rate.
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