Hi Larissa –
Sorry to hear about your commute!
I don't know if any of these areas fit your needs exactly but have you considered NE London, specifically Walthamstow at the end of the Victoria Line? It’s about 35-40 minute journey to Oval, with a change to the Northern Line at Stockwell, which puts you at the top end of you preferred commuting time but it is on a tube line and has an added bonus of also having a mainline station into Liverpool Street, which you are already used to (and very handy in case either line is out of action).
I’m not a driver, but looked up driving times to Upminster online and it looks like the journey from Walthamstow would take about 30 minutes or so (and it would be against rush-hour traffic)
There’s also an overland train to Barking, where you can change to the District line to Upminster if your husband found himself without the car for a day.
Many of my colleagues live in Walthamstow and are generally happy there, especially the old bit east of the station and it’s less expensive comparatively to East London neighbourhoods without a tube connection
To the east of Walthamstow is Chingford, near Epping Forest. No tube but an overland train into Liverpool Street and a very nice, feels small town-ish with a nice high street.
I also have a few friends in Leyton/Leytonstone on the Central Line. We visited a few weeks ago and the house they bought was quite nice and the area seems fine, though I’m not that familiar with it. If I had to live east I would consider it a possibility.
One other area that comes to mind is Bow on the District, Hammersmith & City tube lines plus DLR. It’s gotten expensive with spillover from Bethnal Green but you may be able to find something decent. Very handy to Victoria Park.
good luck with your search