Damn, I was trying to think of a way to combine it with the Thameslink
Moorgate branch and the Aldwych Shuttle.

...via the Jubilee platforms at Charing Cross?

He-he... you are both wrong! ;-)

Aldwych tunnels should be used by new combined Hammersmith&City/Circle
service, which should be named Spiral and should go
Hammersmith-Paddington-Edgware Road-Farrington-Liverpool
Street-Monument-Victoria-Bayswater-Edgware Road{another set of
platforms}-{Marylebone}-{Goodge Street}-Holborn-Aldwych
(new parts are in { } )
(and yes, I know this is impossible, because Holborn-Aldwych part is
tube and not subsurface...)

And Jubilee platforms at Charing Cross should be used by DLR.

OR

Another stupid suggestion would be to create "smaller Circle" of
Waterloo-Bank-Aldwych-Holborn-Green Park-Charing Cross-Waterloo,
which will include entire Waterloo&City line, and both Aldwych and
Jubilee platforms at Charing Cross :-P