CoasterjunkieX

Well dang it. I thought I had finally figured that one out. Thanks for digging that out of the example, it's probably the longest example block in the book.  Does finally puts some things to rest, though.  As for the "simulationist" method you talk about, that's at least covered with an optional rule on p. 127 with "point-blank revisited."

Originally, I ruled the bonus/penalty cancelled as well, but after much research on this topic, my final finding was CoC does not provide rules for shooting at an enemy you are engaged in melee combat with simply becaue the rules don't intend for you to be able to shoot someone you are in melee with.  If you are engaged in melee, you must use a fighting(x) skill.  The rationale seemed to be that if someone is close enough to engage you in melee, they are close enough to disrupt your attempt to shoot them and you have to resort to melee attacks.  I can't recall atm what my conclusion for "shooting someone you are not in melee with while you are engaged by someone else" was, but I think I still allowed that.

Disengaging takes an action, but automatically happens (unless you are playing pulp). So assuming you are slower than an enemy but they do not have a dex 50 higher than yours, this allows you to disengage then shoot at the +50 dex bonus before the enemy can act.  If you are faster than an enemy, I think you can get locked into a disengage-engaged loop, but hopefully you already shot them on round one?

I can at least help with some of the handouts.  They're linked on the product pages for The Two-Headed Serpent and Doors to Darkness.

Two-Headed Serpent: https://www.chaosium.com/content/FreePDFs/CoC/CHA23125 - The Two-Headed Serpent/CHA23125 - The Two-Headed Serpent Keeper Resource Pack.pdf
Pulp Cthulhu Sheets are here: https://www.chaosium.com/cthulhu-character-sheets/

Doors to Darkness Handouts: https://www.chaosium.com/content/FreePDFs/CoC/CHA23148 - Doors to Darkness/CHA23148 - Doors to Darkness Handouts.pdf
Doors to Darkness Pre-gens: https://www.chaosium.com/content/FreePDFs/CoC/CHA23148 - Doors to Darkness/Doors to Darkness Pre-Generated Characters.pdf

Seems Pulp Cthulhu and Terror Australis don't have a handout pack linked.  You should be good with the other two though!  Some other packs can be found on the itch.io page as well: https://chaosium.itch.io/.  Sadly, still no Pulp Cthulhu or Terror Australis there either.