Reconstruction methods can absolutely improve this. They can add information that it expects to be there so the 'fine' details are better resolved much like a native high resolution implementation. It is an actual high resolution image at the end of the day.Well shimmering is a problem of highly detailed games. Especially if you can't use native resolution it gets more and more obvious. But the problem will remain. The smaller the details the more pixels will shimmer in motion. Reconstruction techs don't make that problem really better, they might just hide that problem in favor of other problems. The only thing that really helps with that are higher resolutions (e.g. "inverted" VRS could help, not to decrease resolution of such points but to increase the resolution), lowering the details (e.g. through a more aggressive LOD system) or blurr the image a bit (last one is the thing why TAA might help a bit). But even that at some point it will again be visible. HFW is a bit special there because it also has extreme contrasts in one picture, this make such detail-shifts much more visible.
But Forbidden West is using a slightly lower resolution. 1800p reconstruction and then upscaled is definitely not gonna be as good as 2160p reconstructed with no upscaling necessary. Combined with what's probably just not the best reconstruction method nowadays(checkerboard), I can see this potentially being the issue here as a whole.