Sorry just saw this so I guess its too late, but I think something similar came up before, and the main problem is that Fratton to Winchester via Southampton is not a valid route. (Was it ever?) I haven't time to check out all the fare permutations, but I think one option is to buy a ticket from Fratton that will allow travel either via Netley or via Botley, so the obvious would be Fratton to Southampton Airport (Parkway); and combine it with an Eastleigh to Winchester return.
So your travel would be Outward Fratton > Eastleigh, then break at Eastleigh and use the separate out and return to/from Winchester, resume outward journey at Eastleigh to Parkway, then switch to your return journey via Southampton Central and break your journey there.
Another option is to use a Fratton to Winchester return and on the return journey go from Eastleigh to Fareham the long way round using something valid both ways (Botley or Netley), such as an Eastleigh to Swanwick off-peak day return. Here you'd be breaking your Eastleigh to Swanwick at Southampton Central on the outward, then returning from Swanwick as far as Fareham where you'd be valid again on your return ticket from Winchester to Fratton.
When doing this, don't assume the gateline staff at Central understand the concept of break of journey either...
Edited cos now thought of another way. Fratton to Southampton Central return is valid via Eastleigh, or the usual route via Netley, so you could use that with an Eastleigh to Winchester return as well.
