If 4tph to Reading is viable again then a service pattern like this is probably best:
xx:03 Windsor semifast (Vauxhall, Clapham Jct, Putney, Richmond, Twickenham, Whitton, Feltham, Ashford, Staines, all stations)
xx:06 Waterloo via Kingston (Vauxhall, Clapham Jct, Wandsworth Town, Putney, Barnes, Mortlake, North Sheen, Richmond, St Margarets, Twickenham, Strawberry Hill...)
xx:12 Weybridge via Hounslow (Vauxhall, Clapham Jct, Wandsworth Town, Putney, Barnes, all stations via Hounslow, Feltham, Ashford, Staines, Egham, Virginia Water, Chertsey, Addlestone)
xx:15 Reading fast (Vauxhall, Clapham Jct, Richmond, Twickenham, Staines, Bracknell, all stations)
> overtakes xx:12 between Clapham Jct and Barnes.
xx:18 Reading semifast (Vauxhall, Clapham Jct, Putney, Richmond, Twickenham, Whitton, Feltham, Ashford, Staines, all stations)
xx:21 Waterloo via Twickenham (Vauxhall, Clapham Jct, Wandsworth Town, Putney, Barnes, Mortlake, North Sheen, Richmond, St Margarets, Twickenham, Whitton, Hounslow...)
xx:27 Waterloo via Hounslow (Vauxhall, Clapham Jct, Wandsworth Town, Putney, Barnes, all stations via Hounslow, Whitton...)
xx:33 Windsor semifast (Vauxhall, Clapham Jct, Putney, Richmond, Twickenham, Whitton, Feltham, Ashford, Staines, all stations)
xx:36 Waterloo via Kingston (Vauxhall, Clapham Jct, Wandsworth Town, Putney, Barnes, Mortlake, North Sheen, Richmond, St Margarets, Twickenham, Strawberry Hill...)
xx:42 Weybridge via Hounslow (Vauxhall, Clapham Jct, Wandsworth Town, Putney, Barnes, all stations via Hounslow, Feltham, Ashford, Staines, Egham, Virginia Water, Chertsey, Addlestone)
xx:45 Reading fast (Vauxhall, Clapham Jct, Richmond, Twickenham, Staines, Bracknell, all stations)
> overtakes xx:42 between Clapham Jct and Barnes.
xx:48 Reading semifast (Vauxhall, Clapham Jct, Putney, Richmond, Twickenham, Whitton, Feltham, Ashford, Staines, all stations)
xx:51 Waterloo via Twickenham (Vauxhall, Clapham Jct, Wandsworth Town, Putney, Barnes, Mortlake, North Sheen, Richmond, St Margarets, Twickenham, Whitton, Hounslow...)
xx:57 Waterloo via Hounslow (Vauxhall, Clapham Jct, Wandsworth Town, Putney, Barnes, all stations via Hounslow...)
I'd close Queenstown Rd to simplify the operation of the Windsor lines since the Northern Line extension to Battersea Power Station serves the area from Waterloo and Southern services to Battersea Park serve the area from the south/west by changing at Clapham Junction.
I'd also call everything at Vauxhall to further simplify the service pattern to have everything run at the same speed to Clapham Junction.
The Weybridge via Hounslow trains running 3 mins before the Reading fasts means they join the Feltham to Staines section pretty much exactly in the middle of the Reading semifast and Windsor services, therefore not causing any conflicts.
The Waterloo via Kingston services currently leave at 03 and 33, so with the closure of Queenstown Road and a slight speed up, the 06 and 36 times should mean they slot into their current slots on the SWML, meaning a recast of services on the SWML will not be necessary.