Now I won't get into fantasy timetable land but the following destinations might work
Except you just did exactly that (!)
INV, BHD, NCL, and NQY have no connection to Canary Wharf and the City. BHD and NQY have both been tried before and both failed, Belfast very badly quite recently. NCL just about worked before the financial crash then once the sweetener route opening period was over, it just wasn't viable on a 29 seat J41. If they can't begin to fill a BE DHD from LGW that sits idle half the day, LCY is not going to make it better. INV will get left to the locos and the only one I think might be worth a bash, is Guernsey.
The issue here that might change matters is some form of sale or consolidation around the fate of CityJet.