I wouldn’t make it a “monster” but more of a “monster template” that can be added to NPCs in a manner similar to how Half-Dragon is a template that can be added.

Makes sense Haravikk. I'm learning slowly that, to make this, or I'm guessing anything I might want to work on in the future, available for wide use, I need to think more in terms of generalities and leave the to specifics to others. 

I think what you've described amounts to a variant.  Which is awesome, and I think a monster would be a variant.  I would add that I think this variant should be flavored to be able to change between the souls at will.  A bit OP, but OP is more acceptable for monsters than PCs. 

Ok.  After our Saturday session. I'll 'finalize' the one begun at the top of this string and set it as a feat.  Then, I'll play with what you've got above and try to list it as a monster.  If I'm  successful, I'll also see about building the other variant that another DM evolved, that allows the inactive souls to possess others.

I am going to add Turn Resistance as well. Comes straight from the lich abilities...alludes to the foundations of the Construct, but also makes this undead thing something that needs be fought, rather than just turned, should a party discover its actually undead.

I've done some trimming and conferred with the players and we've agreed to use the following going forward.  It trims the creation of specific lore, cleans up how items are handled, and changes what triggers an 'end of day', to extend the amount of time an adventure day can continue.  Should be more enjoyable to play.  We'll see how it goes.

I've also codified a few variants of the Lastoa'giza, that are geared towards being used purely as monsters.  I'll post those separately. 

Lastoa'giza - the Faithless

Description:  Lastoa'giza are medium-sized, humanoid-shaped, inert Constructs powered by radiant energy.  At the core of the Lastoa'giza is a phylactery which can hold multiple undead souls. The Construct transforms into the form of one of its souls, allowing the soul to experience Second Life.  (A DC 25 Arcana Check is needed to detect exactly what they are)

The Souls: Each soul of the Lastoa'giza is a fully devrloped individual; complete with race, class, abilities, feats, history and equipment. Each soul in a Lastoa'giza must learn its purpose through experience. Once in the phylactery, souls retain separate consciousness, and each have their own perspective on all the Lastoa'giza perceives.  Though only one soul at a time can be active, all of the souls in a phylactery share the raw perceptions of the active soul.  The Souls also share some of their dreams.

Alignment:   Each soul retains its Alignment as per in life.

Second Life: Triggered by radiant energy, after a long rest, the Lastoa'giza randomly selects one of the souls, in turn, in its phylactery, as the active soul.  The Lastoa'giza then transforms itself into the active soul's body, including all items that body last wore or carried, until a long rest is taken or the soul dies. At the beginning of a long rest, the active soul returns to the phylactery, and the Lastoa'giza assumes its inert construct shape, absorbing all items last worn or carried.  Lastoa'giza can only take long rests between the hours of dusk, and dawn. True death - Upon reaching 0 hp, and failing its death saving throws, the active soul is truly dead and can not return to the phylactery, and the Lastoa'giza assumes its inert construct shape. The following day, the Lastoa'giza will randomly select one of the remaining souls in its phylactery to be the active soul. This cycle will continue, until the phylactery is empty, the Construct is damaged beyond functioning, or the phylactery is destroyed. 

The Dreams: The souls of Lastoa'giza are chosen because they are faithless. During a long rest, they are tormented by dreams of death and and the horors of after-death (both their own and other Lastoa'giza near them) until they find faith.  The Lastoa'giza also may recieve instruction in their dreams from entities to which they own a debt, for being allowed to be Lastoa'giza.  Failure to resolve or escape these dreams leads to the eventual destruction of the souls in the Lastoa'giza

Limited Healing:  While in their natural form they are Constructs, and can only be healed or repaired by a Wish spells, or by their creator.   While shapechanged, they count as Undead for both detection and healing. 

Resurrection:   If the gods allow it, only a True Resurrection spell can raise a soul in the phylactery.

Resistance: The Lastoa'giza has advantage on saving throws against any effect that turns undead.  Also has resistance to necrotic damage

Variant Rules: Lastoa'giza require three elements; a Construct with a phylactery, at least one willing faithless soul, and the joining of the soul to the phylactery must be sactioned by at least one other worldly entity or god that has dominion over the soul.  A variety of Lastoa'giza have been and will be created to suit the needs and whims of their creators.

Looks like True Death didn't end up on its own line there, but overall this is much clearer and more accessible, and I think it should play in a really interesting and fun way.

Much better.

Thanks to everyone for the comments.  We'll see how it goes.  Next session in two weeks.  Cheers.