Can you spot what's wrong with these DWV lines?

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hershpersh

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Hello! Assuming the PVC pieces are all primed and glued properly and at the correct slope, what is wrong with this bathroom DWV design for a toilet, shower, tub (furthest at 7' from stack), and sink? 2 Pictures show actual pvc mock up I made for toilet/shower/tub and last is a photoshopped photo for sink drain and vent tie-in. 13" behind the toilet is an existing 3" san-tee into the main stack, which is dedicated to this bathroom (it comes up from the basement and vents up through the roof above this bathroom).

I'm a single mom with over a decade of previous experience in general construction and I had a licensed plumber tell me this can't be done. He said he could do it correctly for only $2,400 and he would have to drill through five floor joist locations and the bottom wall plate would be cut for the sink drain. I'm not a plumber, but I don't believe it. Why wouldn't this work (South Carolina, IPC code)? The tub and shower drains are sized at 2", sink drain is 1 1/2" and ties back in above the flood/fixture line to vent. My design minimizes interference with floor joists after having to sister and repair previous damage done by someone else's hack job running drain lines. Thank you greatly in advance for any feedback! I can't find a local plumber willing to consult for a fee without doing the entire job.
 

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