I like to very gently polish all of the contact surfaces of the firing pin assembly and when possible the bore that it rides in. I also gently radius the leading edges of those surfaces on the FP and the cocking piece. Not the actual cocking face(s), but those surfaces that ride in the bore of the bolt or shroud during the FP's movement. I usually use a Cratex "stone" to do this work on the FP. Note that those surfaces on the FP to be polished include where the spring can touch it, not just where it bears on it.
A coil spring is a torsion bar, it twists as it is compressed and relaxed. Run a Sharpie down one in a straight line while it is relaxed and then compress it and look at your formerly straight line. I know what you'll see, but I've not done it to one of these springs in particular. Also notice how the spring can have 'waves' in it when compressed. If you look at a high cycle FP spring you can see where these waves have worn the high nodes on the bolt's bore.
Given that the FP is fixed & can't rotate I expect there to be some minor rotation of the ends of the spring. It could be that a carefully sized bronze thrust washer between the spring and the FP, or the spring and the shroud, or both, would add some small consistency improvement in the FP's motion. In the same vein, the ends of the spring should be carefully de-burred and polished, particularly the very ends of the wire where the mfg process has no doubt left it a bit rough.
Were I building rifles in small production runs I'd look into having the FP's Superfinished or possibly NiB coated. I doubt either is cost effective for one or two at a time. If Superfinishing it might not hurt to have the spring done too. I'd research that before having it done, but I'd expect a spring to benefit from such work.
Since the Rem cocking motion requires rotation of the bolt shroud's threads in the bolt body I like to lap those threads so that they move smoothly and without any hesitation or grittiness. Same for the cocking surfaces, I like to lap those to each other. And I've been known to lap the primary extraction surfaces.