Here is my approach, and IC use:
Textbook example, it is very fast, and so avoid (those) analog parts, at least directly into IC. Please try look up the CD-4020, that's a good long interval.
I noticed a lot of emphasis, on direct results: "... Such and such, Simulator didn't look good, or SPICE failed..."
Good to run and evaluate, don't take it bad. Just maybe more, slow detail. Here is an example: "I say a circuit for 300 hz square wave. It looks backwards, wasn't that a 'pull-up' circuit ?
That is a maybe, partially navigating as you learn.
Once you go all digital, try the classic:
Rising Edge, to short pulse out:
Place input to NAND IC gate.
Take also into an inverter, just use another NAND.
Run inverter into NAND, other input.
That will spit, briefly, (downward), when the
occasional edge happens.
You got one part... So...
By the way, I always try to put a bit more delay, just
just string into pairs of gates, to extend the pulse
time.
Thanks