I would try the following to achieve a closer fit at the back of the jacket:
1. Reduce the across shoulder measurement so that the roll of the sleeve is closer to the top of the arm. (-1/2")
2. Reduce the back armhole by slashing pattern horizontally from centre back to armhole.(-1/2")
3. Reduce the upper back sleeve by same amount.(-1/2")
4. Consider adding a back shoulder dart. This helps to fit the curve of the back. the dart could be 3/8" to 1/2" depending on posture.
5. Add a vertical fitting seam/dart at the side back that runs from hem or close to the hem to the armhole. Refer to a classic mens fitted suit jacket for shape and location.
Hope this is helpful.
I wish I knew how to add a drawing to the comment box!
Good luck! I admire your will to do the task long distance.

The first thing my mother sewed for herself when she came to Canada in the 1950's was a fitted dress with boat neck and three quarter length sleeves. She used a very good quality black cotton brocade...a clssic for sure. She wore the dress often but when no longer in fashion could not part with it for sentimental reasons. Today my 18 year old daughter wears the dress with pride. She says it is the perfect "Audrey Hepburn" look.

It is a beautiful dress.
I made a similar dress for my daughter recenty but I had so much trouble with the hemming of the organza. How was the hem finished?