My first reaction would be to figure out why there is a one inch gap.
Do you have decayed or rotten sills? Termites or ants?
Or is it just settlement...I would find out before I put any money into something which may have to be removed to repair issues found later.
Sometimes you get in there to jack something up only to find there is nothing there to jack.
Good luck with your project...I love new kitchens.