I've not cycled that area much, but have driven bits of it a fair amount.
The tiny bit of the A3057 you've got coming out of King's Somborne includes a section which is uphill, and is likely to have accelerating motor traffic in combination with blind corners. If you're keen to hit up some rough surfaces, then it might be worth considering staying on the National Bridleway to turn North out of King's Somborne, then cutting across to join the old railway line trail to join back onto your proposed route at Horsebridge. The catch is Cow Drove Hill, but...
Other than that, the other main thing I notice is that your route already includes Carlo's Icecream in West Wellow