David : Hardware Part Niumber 381943 that you noted is a flat, rectangular, spring nut for a 3/16" stud (first picture attached). The 375942 that you noted is a stamped steel, cone and flange, hex. 10-24, threaded nut. Like the others, I have only seen smooth, non-threaded studs on the center covers. Possibly, the early reproductions might have been threaded, but like the originals that I am familiar wiyth, most, if not all, current reproductions have the smoothg stud, and come with the flat, spring nuts.
However, alot of used originals are seen to have the stamped, self-threading, nuts (next picture attached). Possibly this was one of the many running changes during 1967, or maybe Service Parts came this way (?). Jim notes the 373503 stamped self-threading nut as "Alt" in his Hardwarew Spreadsheet for 1967-68, although IO'mnot sure where the alternate designationoriginated.
If I were installing the cover, I would use the flat spring nut, if i envisdioned never having to remove them. They are easy to install (they just push on), and will hld the cover tightly against the joint ; but,they are a "bear" to remove,ewspecially without breaking the stud.
If you think that "down the road", you might want, or have to) remove the cover, I would opt for the stamped, sewlf-threading nuts. To reduce the chance of breaking the stud, I would pre-thread it with the self-threwading nut. Hold trhew stud with a needle-nose vice grip or similar, just below the nut, and start the nut on the stud. Keeop moving the vice grip downas threads are cut. THis may take some of the torque off of the stud. Self-thgrewading nuts typically don't cut very deep threads, so i you get one for a 3/16" stud, it should be OK.
Hope this helps.
Bob