It's unclear, but I would say yes, you can benefit from multiple copies of Shield (with some caveats).
As you've pointed out, if you play an Elf Wizard who takes the Otherworldly Magic and Sorcerer Dedication feats (taking the Draconic bloodline or any other one with arcane as its spell list), you can have Shield as your OM cantrip, both SD cantrips, and you can prepare Shield as all of your cantrips for the day if you wish.
Determining whether casting one copy of Shield prevents you from casting the others after using the Shield Block reaction is difficult as Shield is the only spell in the list that has the "can't cast again for X minutes" restriction and there's little precedent for this situation that I've been able to see, but consider that preparing multiple copies of a levelled spell allows you to cast that spell in its entirety once for every copy you have prepared on a given day, treating each copy as its own distinct spell. Now let's look at the wording of the Shield spell:
You raise a magical shield of force. This counts as using the Raise a Shield action, giving you a +1 circumstance bonus to AC until the start of your next turn, but it doesn't require a hand to use.
While the spell is in effect, you can use the Shield Block reaction with your magic shield. The shield has Hardness 5. After you use Shield Block, the spell ends and you can't cast it again for 10 minutes. Unlike a normal Shield Block, you can use the spell's reaction against the magic missile spell.
I would say "the spell" and "it" refer only to that specific copy of Shield, and that each one would have its own 10 minute timer after the reaction is used. I unfortunately can't back this up with a passage from the rulebook because there's nothing in there about whether multiple copies of a spell are considered the same spell for this purpose, but I'd point out that if you have multiple copies of the same buff spell on one target (Wind Walk for example), Dispel Magic only removes one copy of it even though it ends "one ongoing spell" indicating that each copy is considered separately and the same should apply for Shield.
As Isaac pointed out, the AC bonus wouldn't stack regardless since it's a Circumstance bonus and typed bonuses only apply the highest of those active, and you'd only get to use Shield Block once per round assuming you hadn't used your reaction for anything else, until you'd used it once for each copy of Shield you cast.