Spin polarization in the electron transmission of radicals is important for understanding single-molecule conductance experiments focusing on shot noise, Kondo properties or magnetoresistance. We study how stable radical substituents can affect such spin polarization when attached to oligo(p- phenyleneethynylene) (OPE) backbones. We find that it is not straightforward to translate the spin density on a stable radical substituent into spin-dependent transmission for the para-connected wires under study here, owing to increased steric interactions compared with meta-connected wires, and a resulting twisting of the radical substituent and OPE π systems. The most promising example is a t-butyl nitroxide substituent, which, despite little pronounced spin delocalization onto the backbone, yields a spin-dependent transmission feature which one might be able to shift towards the Fermi energy by additional substituents. We also find that for bulkier substituents, dispersion interactions with the substituent can lead to twisting of one of the outer OPE rings, reducing the overall conductance. As a further potential design consideration, attaching radicals via linkers might increase the possibilities for spin-dependent intermolecular and molecule-electrode interactions.