If I am forced to choose between Eibach springs and anti-roll bars, I would do the springs first. Reason is simple... With Eibach's Pro-Kit springs, both the CG lowering and 10-15% stiffer spring all around will reduce both dive/squat (in pitch axis) and lateral lean angle (in the roll axis). Anti-roll bars only improves the latter.
That said,
aftermarket anti-roll bars do typically allow for roll stiffness adjustment front vs. rear, so if the car tends of understeer excessively, that might potentially help more. Stinger isn't too bad in that regard... provided that you trail brake into the corner to keep weight over the front tires for more grip on corner entry. If you don't do that, no amount of anti-roll bar adjustment is gonna help you.
Practically, if you're staying in FS class, lowering springs are not allowed anyway. Even anti-roll bar you are ONLY allowed one non-stock (front
or rear). So that makes your question kinda moot.
If I were you... if you're serious about chasing cones regularly, I would invest in a set of lightweight wheels and 200 tread wear dedicated autoX tires. That mod is perfectly legal for Stock class and will improve your lap time far more than Eibach springs and anti-roll bars, combined. The stock rims are boat anchors. My lightest AutoX set are Enkei RPF1 18x8.5 weighing 18.2 lbs per wheel.
OTOH, if you just want to have a little weekend fun here and there occasionally, just go with what you've got. Unless you are a seasoned Pro Solo jockey, the slowest part of the whole car is the lump of noodles inside your helmet. Even stock, the Stinger is faster than you are.