Good Evening Bones92,
I think that your jag design has some merit, but is probably a bit over engineered. The idea of using the long screw is not a bad idea. Considering the number of broken off brass thread studs I have seen over the years, using a steel screw would be the best idea.
One time I made a jag that had the cross cuts on the end;could not determine that it made any real difference in cleaning the face of the breech.. However, since my barrels are equipped with patent breeches, that would have meant turning a two diameter jag to match the diameter of the powder chamber and bore. That also meant turning a longer jag; more work than I wanted to do.
Now my other suggestion is to use a flat heat screw and countersink to be flush and flat with the end of the a flat bottom jag. That way you can get the patch flush up against the face of the breech plug. Then you can cross file notches in the face of the jag for perhaps better cleaning of the breech plug face.
Back in the 1980's I made several hundred cleaning rods of 416 stainless steel and the brass jags. Started this at the request of numerous friends who wanted a stronger, less breakable screw on the jag system. For 45 caliber and larger bores. the rod were made of 5/16" diameter s.s. Under 45 caliber, 1/4" diameter s.s. was used.
The difference was that the end of the 5/16" rod was turned and threaded for an external 1/4" - 28 thread. The jag had a matching internal 1/4" x 28 thread. The 1/4" diameter s.s. rod did not have to be turned.
Never had a jag break due to being loose on the rod. In fact nobody ever reported a broken jag to me.
Will write more on this later.
My wife is calling me to dinner, and you definitely would not want to miss my wife's cooking. She is from Thailand, and I am treated to great Thai dishes 3-4 times a week and in between, favorite American dishes she has learned to prepare for me.
I am a blessed man.
My respects to all,
John L. Hinnant
"God and Texas"