So to be clear, the lower u-joint is damaged. Nothing may be snapped, but it sure looks borked to me in more ways than one.
If I'm seeing it correctly, there were at least two problems:
The shaft piece was not properly secured correctly by the set screws, or otherwise installed incorrectly. The shaft piece either slid into the joint space, or too much shaft was left exposed when installed, and during turns, the journals made contact with the exposed shaft, causing them to bend. That explains why the bearing cap is protruded from the fork (this is normally flush, and I see damage to the cap by the retaining screw), and why I can't see the fork in the background...it's bent out of position. The mark on the end of the shaft I was starting to mistake as a set screw indentation, is actually from the fork making contact with the shaft.
The rack was probably not rotated enough. I can see binding marks on the fork that I don't think would have been caused after the journal had started to bend. If the rack was rotated enough, some shaft exposure might have still been ok, as the joint wouldn't have oscillated as much and potentially avoiding contact. Still, the lower joint sees a more extreme angle than the upper joint, so any exposed length is not desirable. Notably, rotating the rack too much can also lead to exposing the shaft (more rotation means less shaft length needed), but again, the binding marks suggest it wasn't rotated enough.
Having purchased and installed several of these links and joints, I know the Woodward joints are high quality. The failure here is from either installation or maintenance, not the part itself.
Are set screws missing? Those should have had threadlocker applied after confirming the steering was aligned correctly. For the upper part that slipped out, is there a set screw groove on the shaft? Are there set screw marks in that groove?
Your best bet at this point is probably to buy a new lower u-joint from Woodward and wait it out. You may also need a new shaft piece, since the damage at the end will make it difficult to remove from the u-joint, and will require some filing to repair in order to re-use, if you can even remove it from the joint (might be easiest to remove the journal first then push the shaft through).
My homework on the Honda joint suggested it wasn't even the right spline count and only conveniently fit because it was slightly oversized and, as a clamp-style, non-cast joint with an opening, could be tightened enough to take up that missing spline. I don't think it was ever clear what model/year it came from, either; some early 90's Accord perhaps. It was also for the upper joint, and your failure appears to be on the lower joint, so it's not going to help you much. Plus, all the DIY steering links I've seen have looked like dangerous garbage, so unless you've got the fabrication skills, I'd stick with what works and ensure that the next installation is done correctly.