Doing shintai first avoids us getting damaged in our regular form.
There is some strategy to this.
Using Shintai later on means that we can avoid giving away too many tricks at once if we don't need to, and lets us basically reset our health track mid fight if we get into trouble. Since dropping Shintai deals 5 unsoakable bashing damage, so if she does beat our ass around the yard we come out into the fight injured for the second round.
You could just as easily claim that taking the extra bashing while injured is a disadvantage as well though.
It comes down to the evaluation of if we think she's likely to bust our Shintai after having fought baseline Molly for a while first, and how much we expect to be hampered by injury debuffs.
We're pretty resistant to that stuff, but still only have a baseline track, so if we fight my inclination would be to order the car to hit as hard as it can, then focus on pinning and disrupting her. While it does that, we draw and apply excellency but not TA. Instead we immediately go for a throat shot with GSNF since we just need to hit to deal 4 Agg damage.
That leaves us with 7 essence, so next turn we pop TA and go for another attack. If we don't need to use IPM that turn then slap her with GSNF again.
Best case we're down to 5 essence and she's eaten a minimum of 8 levels of Agg damage in 6 seconds, on top of whatever lethal damage the car and our first stab do. Worst case she still has to spend part of her action countering the car both rounds, so it should be much easier to get our hits in and avoid hers.
That is probably the point where we pop Shintai if she looks like she still wants to fight since it takes a turn of concentration. If she gets us particularly badly in the first exchange we might want to consider dropping the turn 2 attack for immediate transformation.