The Initial Equipment box only has one row per equipment type, so YEP Equip Core puts that one ring in your first Rings slot and leaves the rest empty. The Change Equipment event command also only goes to the first slot of a type, so it would just keep swapping that same ring.
What I’d probably do is use a Script call in an event that runs once when the game starts. An autorun event on your starting map that turns on a self switch at the end would work:
var actor = $gameActors.actor(1);
actor.forceChangeEquip(5, $dataArmors[10]);
actor.forceChangeEquip(6, $dataArmors[11]);
The first number is the slot’s place in your equip list, counting from 0 at the top. So if Rings first shows up 5th in the list, that slot is 4 (your editor ring goes there), and the next two are 5 and 6. The number in $dataArmors[ ] is the ring’s ID from the Armors tab, and actor(1) should be your main character’s actor ID.
I used forceChangeEquip because it doesn’t need the ring to be in the party’s inventory first. The normal changeEquip does.