You could ask the NHS OT to do some actual assessments. In my experience NHS OT dont like to do assessments, they just say 'difficulties' based on 'mum says'.
The report i quoted was a ind OT, if your school are good at giving help and following recommendations it might well be worth getting an ind OT to assess.
Mine assessed drawing and writing skills, visual perceptual skills ie eye hand coordinations, position in space, copying, visual closure etc, etc. fine and gross motor skills, postural tone and joint stability etc, etc and found difficulties in all areas.
She concludes that he needs direct input from a state registered OT with sensory integration training. A programme for daily integration of movement breaks and a programme to address all of the difficulties highlighted in the report. OT should train staff, staff have to be present at all OT sessions, OT to set IEP targets, etc, etc.
Sounds like the TA is doing a good job, given she has no training, nothing to work with etc.
It would very much depend on what difficulties your ds has with his gross motor skills, as to what exercises you could do.
Ds's school are refusing to give him the help OT recommended, so i dont actually have any programmes.
I have a general sensory diet for ds which anyone could follow, but that doesnt address gross motor skills, its more sensory.
If like ds, you would have to work on all areas of difficulties, working on just one is a bit counter productive, other than doing just general exercises that you are already doing.