I have a 26″ OnOne Inbred 14″ that has been my daughters and my wifes run around bike. It’s in spot on condition, having only ever been used around child friendly green/blues and for going to the shops…it has buckets of standover for someone under 5′ tall and a RS SID 100mm dual air fork with lockout on it.
Hope pro2/Stands Olympic wheels that weigh naff all. If you are interested in that let me know. The current spec is 1x with zee/deore drivetrain/brakes but I have other brakes etc. and 2x would cost £20.
Either way it would come in at waaaay less than your £1k budget even with a new drivetrain and finishing kit.
But importantly an Inbred 14″ with a 100-120 fork is a great frame, with sorted angles, with sensible kit it also ends up being light.
My daughter had one from 8yrs old on 26″ wheels with no standover issues and used it with 24″ wheels before that.
You haven’t said how tall your wife is.
The xs Salsa El Mariachi is really good and super small even as a 29er but it would blow the budget.