If you make a mistake at work, you are expected to feel bad and express that through your body language and speech. If however, you’ve developed more stoic thinking patterns and ask yourself “I made a mistake, but that’s already happened so instead of regretting I’m going to focus on what I can do to avoid that mistake in the future”, you’ll also likely have body language and speech that doesn’t communicate regret in the same way.

Epictetus, one of the more popular Stoics, discusses this in the Enchiridion. In book XVI, it states "When you see anyone weeping in grief because his son has gone abroad, or is dead, or because he has suffered in his affairs, be careful that the appearance may not misdirect you. Instead, distinguish within your own mind, and be prepared to say, 'It’s not the accident that distresses this person, because it doesn’t distress another person; it is the judgment which he makes about it.' As far as words go, however, don’t reduce yourself to his level, and certainly do not moan with him. Do not moan inwardly either."

The Stoic practitioner is to display grief and offer consolation, but avoid allowing this to bring them actual grief too. It's a subtlety I didn't know about until reading into the various Stoic works more and taking an undergraduate seminar on Stoicism. 

If this model is correct, Then we cannot NOT do this.

My point of this post was to ask "Does anyone here have any cognitive science background that could prove useful in investigating this further as to determine if it is worth delving into"

Yes, duration and the specifics of the model are important to understand. What I want to know is if the supporting research was conducted in an effective way and can be trusted as a sufficient bolstering of the model.

To be fair, if the models of belief involving encapsulation are true, then one can technically hold contradictory beliefs as long as these beliefs aren't activated at the same time. Is it possible that dissonance occurs when two contradictory beliefs are activated and held simultaneously? 
In other words, imagine some stimulus prompts two contradictory beliefs to be activated and for them to encounter one another. This would result in confusion and by the model of dissonance, the creature would seek to resolve this contradiction.  
 

This assumes that dissonance is a real thing. 

Back to the Spinozan model, the issue of simultaneously believing contradictory propositions is not an issue for the model, but an issue for the model of beliefs in general.  

To address this " If I say "2+2=4" then a moment later,"2+2=3", what do you predict you'll believe after another second or two?", we simply need to acknowledge that the conscious mind OR other beliefs override the clearly faulty belief of 2+2=3. The process of automatic acceptance is more subtle (according to the model). Both beliefs are automatically held as true, and then whether through conscious change or interaction with previously held beliefs, the apparent false belief is rejected. 

The premise of the model is that ACCEPTANCE COMES FIRST AUTOMATICALLY, and THEN, rejection is a process coming after this in time, possibly from a part of the brain that evolved secondarily. 

"But it does NOT follow that we need to guard our inputs to prevent experiencing these falsehoods.  It just means we should (as in other models) become adept at not integrating them into our long-term reflective beliefs."

I agree with this on the basis that guarding inputs would be far too complicated and may not even be a net positive thing for the system in question.

MORE TO INVESTIGATE:
- How would a situation such as simultaneous exposure to 2+2=4 and 2+2=3 be resolved in the mind?