After advice from the community and the lovely ShadyIbrahim's advice, I was able to finally balance out the weight issues on this plane and make her fly nicely! She'll give a bit of lift without the rockets but she's a beautiful CAS plane, and I loosely based her off of an A10 Warthog, but I eventually had to compromise for putting the engines on the wings, which opened up so many cans of worms.

AG1-4: Fire Missles (pressing a button will fire 2 at once)
AG5: Decouple missle pylons (Gives the plane a bit more lift)

If you want, I find hovering the trim about 10% tends to help keep her steady.

ALSO THANK YOU GUYS FOR THE 120 UPVOTE POINT THINGS. NEVER EXPECTED A NEWBIE LIKE ME TO GET THIS MANY.