I'm nobody's salesperson and don't really care what the OP chooses. I suspect nobody here gets any compensation for whatever the OP chooses. I suspect nobody here goes to the same church should the OP end up having to discharge the firearm during a security threat.
It's all academic as the OP came up with a variety of criteria which may counter what some people would even consider and can result in a handgun some people wouldn't consider. There may actually be no handgun in existence which the OP will find ideal.
There are some great thoughts and comments, so far, on the OP's discussion regarding his thoughts/wants/considerations.
#1 under the heading "SAFETY". I initially thought the OP wanted a manual thumb safety of some sort. In re-reading the OP, the criteria indicates a "light trigger", which is vague as it doesn't indicate a trigger pull weight, is somehow safer. "DOA", which to me means "dead on arrival", I'm guessing, meant DAO, or double-action-only, is arguably not safer, but just different. At the end, the OP would also like 2nd strike capability. 2nd strike capability is yet another arguable want-item which I might address later.
Also, DA/SA, which has been commonly used in handguns like the CZ75; SIG's older-designed P-series, i.e., P229, P226, P220, or others no longer being made; or Beretta M9/92; will have a heavier initial trigger pull, but the subsequent trigger pulls are lighter.
#2 CALIBER. A "caliber which is accurate" is vague and accuracy will also depend on the firearm and shooter, too. Does caliber make a particular handgun less accurate, or will it only make a follow-up shot take longer, i.e., make (longer "splits"?). No need to answer.
"Won't over-penetrate" is also vague. While I believe the FBI protocol in ammo choice is 12" to 18", for most commonly chosen handgun self-defense calibers, there isn't a magic or smart caliber which is so accurate you could shoot without aiming, yet when the (human) threat happens to be hit, will automatically stop before exiting the threat, with the mushroomed bullet just being found in the back of the threat's tucked in shirt once the autopsy is performed. OP may want to merely state what caliber and ammo will be used. If it's .380, which the OP seemed to be favoring, then so state it. Then we can get into the never-ending caliber war.
#3. "Maximizing" being concealable "while still having a full grip". This seems to be in such opposition, it's either a no-win "want" and in the end, will only be known to the OP as to what works. We're all thinking a concealable handgun, possibly in an IWB holster. I don't think anyone suggested an AK or AR pistol (yet).
Maybe I missed it as the thread just keeps getting longer, but a "pistol" may not be the answer. Thinking less literally, there are revolvers (yet more caliber choices) which are often DAO. 2nd-strike capable, once the cylinder goes around. Then there are the non or less lethal "Taser" type products; chemical sprays; and impact weapons, which are totally non-firearm options.
2nd-strike capability. This is both a training issue and a hardware-selection issue regarding ammo and the handgun; and why didn't the round go off. How many strikes are going to be used until it is determined the primer is never going to go off? (rhetorical, don't answer). Just go to the next round &/or reload.
Ending suggestions:
Consider revolvers, too. There are many sizes and calibers to consider.
Consider what Glock has to offer. Most Glocks, if not all, have the ability to be modified with heavier trigger pull weights and even resulting in DAO-type triggers (NY1 and NY2 trigger options; heavier firing pin springs). Of course Glocks come in a variety of sizes with "pinky" extensions commonly used if the initial size seems too small (G42, G43, G43X, G26, etc.). I don't believe the smaller models will have a DAO type result even though the trigger can be made heavier. The G26gen3 will have the older style NY1 or NY2 trigger springs available, however. Again, I believe a heavier trigger pull doesn't make the firearm safer, and might detract from accuracy.