How do I tell when it is time to put my wife in full time care?

I'd say now is the time. Her care is taking too much of a toll on you for one thing, plus she has so many needs that one person is unlikely to be able to provide for all of her care day in and day out.

I'd definitely start looking for a quality care nursing home close to you. Then you can visit and monitor her care, but still concentrate on quality time during visits rather than the physical care you must do now.
Take care of yourself, too.
Carol

Yes, it is time to have the conversation with her MD about nursing homes. He can also prescribe meds to alleviate her depression. Visit a NH nearby and take a look around. Is it clean? Ask to try a meal, they will do that.
Once she is there, you can enjoy her company and leave the hard work to the professionals. She will need time to adjust, but most residents bond to their caregivers quite nicely.