One thing I have found is our children want our attention far more than the gifts or toys. My daughter is the same age as yours. She will be 7 in June. She wants mommy. Her worst behavior is when I am not giving her attention. You said she quiets down with the screaming fits when you spend time comforting her (unless I misread that) and then soon acts up when it's over. Maybe try spontaneous cuddling or attention when she is being good. Ignore the screaming fits. My daughter used to do that but stopped after I walked away until she was calmer.
Do you read to her at bedtime? I try with my daughter but it doesn't always work out. I do, however, read to my 9 year old son in bed every night. I started because he was really difficult to settle at bedtime. It's fantastic bonding time. He wouldn't now miss it for the world. Biggest punishment? If you don't settle and get in bed, no reading tonight. And I follow through. In a year or so he's only missed a night or two.
You've had your daughter for a year now. Consistency is important. And I'd say counseling is a great idea. She may have a lot of anger and confusion bottled up that she just doesn't know how to handle.
Hang in there. I'd say do the party.