The evolution of the low-temperature electronic structure of the cuprate metals from the overdoped to the underdoped side has recently been addressed through angle-dependant magnetoresistance (ADMR) experiments in La1.6-xNd0.4SrxCuO4. The results show a striking difference between hole dopings p=0.24 and p=0.21, which lie on either side of a putative quantum critical point at intermediate p. Motivated by this, we here study the theory of ADMR in correlated layered materials, paying special attention to the role of angle-dependent quasiparticle weights Zk. Such a Zk is expected to characterize a number of popular models of the cuprate materials, particularly when underdoped. Further, in the limit of weak interlayer hopping the quasiparticle weight will affect the c-axis transport measured in ADMR experiments. We show that proper inclusion of the quasiparticle weight does not support an interpretation of the data in terms of a (π,π) spin density wave ordered state, in agreement with the lack of direct evidence for such order. We show that a simple model of Fermi surface reconfiguring across a van Hove point captures many of the striking differences seen between p=0.21 and p=0.24. We comment on why such a model may be appropriate for interpreting the ADMR data, despite having a large Fermi surface at p=0.21, seemingly in contradiction with other evidence for a small Fermi surface at that doping level. © 2022 American Physical Society.