Intimidating Prowess and Unchained Barbarian's Intimidating Glare Interaction

Question

So, I want to make an Intimidating Unchained Barbarian, and I saw that Intimidating Glare got changed. Which means that my go to feat, Intimidating Prowess, allows double your Strength modifier to Demoralize??? Because this is how I am interpreting the rules: Demoralize is an Intimidate(CHA) check. Intimidating Prowess makes it Intimidate(CHA+STR). Intimidating Glare makes it Intimidate(STR[replacing CHA]+STR). Am I right? Or does replacing CHA with STR by using Intimidating Glare invalidate Intimidating Prowess since there is no longer a CHA modifier to add to??

Intimidating Glare (EX): The barbarian adds her Strength modifier in place of her Charisma modifier on all Intimidate checks to demoralize a foe. She can attempt an Intimidate check to demoralize an adjacent foe as a move action instead of a standard action. If the barbarian successfully demoralizes an adjacent foe, that foe is shaken for the remainder of the barbarian’s current rage.

Answer 1

You would only get your strength bonus once.

If we look at Intimidating Prowess, we can see:

Benefit: Add your Strength modifier to Intimidate skill checks in addition to your Charisma modifier.

While Intimidating Glare states:

The barbarian adds her Strength modifier in place of her Charisma modifier on all Intimidate checks to demoralize a foe. She can attempt an Intimidate check to demoralize an adjacent foe as a move action instead of a standard action. If the barbarian successfully demoralizes an adjacent foe, that foe is shaken for the remainder of the barbarian’s current rage.

At this point, the barbarian would add their strength bonus to the check (due to Intimidating Prowess), and they would replace the Charisma bonus normally used for intimidate checks with their Strength bonus. This makes it seem like they would add twice their strength bonus to the check.

However, we have an FAQ stating:

Do ability modifiers from the same ability stack? For instance, can you add the same ability bonus on the same roll twice using two different effects that each add that same ability modifier?

No. An ability bonus, such as "Strength bonus", is considered to be the same source for the purpose of bonuses from the same source not stacking. However, you can still add, for instance “a deflection bonus equal to your Charisma modifier” and your Charisma modifier. For this purpose, however, the paladin's untyped "bonus equal to her Charisma bonus (if any) on all saving throws" from divine grace is considered to be the same as "Charisma bonus (if any)", and the same would be true for any other untyped "bonus equal to her [ability score] bonus" constructions.

Since both abilities would add your Strength bonus, it would fall under this FAQ and only one instance of your strength bonus would be applied.

If Intimidating Prowess instead applied "a morale bonus equal to your Strength modifier", it would work with Intimidating glare to give your effectively double your strength bonus. However, it does not, and thus doesn't work with Intimidating Glare.