The Simurgh cannot accomplish bullshit against us without resources. In this case, by resources, I mean tinkertech, someone to mindrape, or pre-existing neuroses to exploit. Lacking those, she's limited to her equivalent of hand-to-hand - telekinesis with asteroids and other random detritus, enhanced by her thinker powers. While she's good at hand-to-hand, she's not good enough to beat The Avatar, especially not while he's got a use of Fate Manipulation spare. Furthermore, if we can get her to that state, time becomes on our side since we recover Fate Manipulation charges on something like a daily basis, while nothing else tactically significant occurs until a week from now - and she can't comprehend anything relating to Fate Manipulation, so her entire strategy would be badly skewed.
That's roughly the scenario we get to with a successful Clearing of the Board. I think she still has a few other minor tinkertech knickknacks around, but nothing big enough to matter when we're not making stupid mistakes. We can beat her without ever going below our current number of Fate Manipulation charges, so we always have a massive margin for error.
On the other hand if we go with tipping Murphy's hat, we have a significant odds of pulling of an immediate win. Only significant though, because we don't know where her core is (IIRC we've determined that it's not in her head or her torso... leaving arms, legs, and wings), and the maneuver is fairly complicated to begin with and our Fate Manipulation would be doing double duty, making sure she got hit and making sure we *didn't* get hit. If we failed that roll... she'd probably be damaged, but a damaged Endbringer retains full effectiveness, especially the Simurgh who doesn't actually rely on her limbs for anything. We might or might not be damaged, might or might not have lost the initiative, and would be running on fumes as far as our Fate Manipulation goes. Not good odds.
It looks to me like a choice between a very high chance of winning a slow fight, or a medium chance of winning a quick fight. We're not in that big a hurry. We shouldn't risk our existence without a better reward than speeding up the battle.