M.M.
I have to say, full strength vinegar left to soak for about 5-10 minutes is fantastic at making grout look new again. However, you need to scrub with a tooth brush. You can avoid hands and knees by just sitting on the floor and working in the space next to you as you leave the vinegar to work it's magic on the other side. Or you could get a low stool and sit on it to do the work. I haven't found any cleaner that works without having to scrub or wipe up afterwards. You could always hire a cleaning service and ask them if they will deep clean. Good luck.