Is rerouting the waste line really necessary
Could be related to fixture units meaning the old line has too much stuff dumping into it to accommodate the new bathroom OR could be your proposed 14' run is too far to wet vent back to the stack (unless you're already planning on a separate vent, then it doesn't matter.  

If this is a 4" stack you should be fine on fixture units (unless you have 6 bathrooms upstairs) but you could be pushing the limit on wet venting at 14'.  Therefore, run your waste line into existing as you suggest and then run a 2" vent out the back of the closet bend.  In your illustration the plumber's proposal on the opposite wall would need a vent anyway so I assume it is going vertically?  Run the 2" up that chase instead.  I may be missing the boat here, hope this helps.

Personally, I'd redesign the bath to avoid dynamiting the home theater and digging a mine shaft down to the main, that is guaranteed to end in tears.