Eeee, looking over the lists, I can see why you're having troubles with them. Well, I have some suggestions, and I'll post them here. Feel free to use them, ignore them, be inspired, what have you.
Also, I will admit right up front, I'm really stretching to make some of these work.
Cover: Drives the bearer to subconsciously notice and intercept attacks aimed at those companions nearest to him/her.
HP Plus: Increases the bearer's natural resiliency, allowing them to take more injuries before suffering negative effects.
MP Plus: Stores magical energy, providing a sort of reservoir for spellcasters to draw upon.
Mega All: Messes around with the fabric of reality itself, causing actions to be applied to multiple targets.
Counter Attack: (Remove this one?)
HP<--> MP: (Remove this one?)
Long Range: Alters reality around the Materia, causing the item it is slotted to to increase its size, without increasing its weight or throwing its balance off.
Pre-emptive: Grants the bearer the ability to sense hostile intent, allowing them to notice opponents.
Chocobo Lure: Makes the item this Materia is slotted to smell like Gysahl Greens, which will draw the attention of Chocobos.
Enemy Lure: Makes the item this Materia is slotted to smell of blood, drawing predatory animals towards what they believe to be a fresh kill.
Enemy Away: Makes the item this Materia is slotted to smell of some foul, harsh chemicals; few creatures will brave the noxious odor to attack the bearer.
Gil Plus: (Remove this one?)
EXP Plus: Alters the bearers mind to make learning easier.
Luck Plus: Has a small, reality altering effect that causes results to better benefit the bearer, to a small degree.
Magic Plus: Enhances the bearers spiritual power, making their magic stronger.
Speed Plus: Enhances the bearers musculature, allowing them to move more quickly.
Underwater: Gives the bearer gills, allowing them to breathe underwater.
Steal: (Remove this one?)
Morph: This Materia causes its bearer to take on the form and abilities of certain creatures, the memories of which are sealed inside the Materia.
Enemy Skill: The bearer of this Materia is able to perfectly mimic the abilities of others that they observe, drawing upon magic if necessary.
W-item: (Remove this one?)
W-Summon: Synergizes the bearers soul with summoned entities, allowing them to summon multiple ones at the same time.
Mime: (Remove this one?)
Manipulate: Magically disables the targets will, turning them into little more than a marionette for the bearer of this Materia.
Deathblow: (remove this one?)
Throw: (Remove this one?)
Sense: Allows the bearer to intuit the general strengths and weaknesses of a target.
W-magic: Synergizes the bearers soul with the magical forces of the world, allowing them to cast multiple spells at the same time.
Slash-all: This Materia creates an invisible shockwave with every attack from a weapon, which travels and deals damage to those around the target.
Double-cut: Causes the weapon this Materia is attached to to deal twice as much damage as it should (same effect as a consecutive attack; else, get rid of it?).
I realize I'm not much of a help, but I hope this is something you can make use of.