In California when the mix is over 2500 psi for structural reasons there is a deputy inspection required and a break test as well. It sounds like that is not the case where you are?
We usually use epoxy in these situations. Epoxy bolts typically require a deputy inspection. I don't think wedge anchors do. Check with your inspector to confirm.
I was banned as well. I called corporate and informed them I was a contractor they cancelled my ban and made it so I would not have any further issues.
Don't leave the sistering to screws. It needs to be nailed together. The shear value of a nail is much greater than a screw. Don't hand nail it you will vibrate the joist and crack the plaster. Rent or borrow a gun nailer and shoot it together.
Where are you located In so cal? Reason I ask is I'm a general in so cal and I may be able to give you a recommendation of a concrete guy depending on your location.