1968 340 push rod issue

Um no, the pushrod length has nothing to do with the nuts backing off.
The only thing that can cause the nuts to back off is that they, the adjusters, or even the arms, are no good.
But the thing that causes ticking on rockers in the which the nuts are NOT backing off, is another matter. You got three/four choices;
1) the pushrods are hitting the tunnels in the heads, or
2) the lifters are not working properly, or
3) the lobes are falling into the pan,
4) Zero lash on hydraulics is too loose; any wear occurring anywhere in the valve gear will immediately show up as ticking.
Typically, we tighten hydraulics 3>4 turns. But some of us run at 1 turn or even 1/2 turn after break-in. ; once the lifters are "broke-in". At half a turn, I might have to adjust them maybe every two years.
I run at this minimum lash, because if the lifters ever pump up, there is no chance that the pumped-up lifters can ever drive the valves into the pistons. Thus, I can blissfully rev the engine until the rods fly out the side. My stock rods seem to be good to 7200, so that's when I shift. Your results may vary.

Therefore, if this engine keeps developing ticking, on rockers in the which the lash-adjusters are good, you gotta suspect lobes going down.
Ima thinking it's time to inspect the lifter feet.