Sounds a lot like our shop. We have weekly management meetings and that item seems to jump on the agenda when it gets crazy busy like it is now. What eased the pain a bit for us is building a fleet of loaner cars so that if you have to keep a car overnight, the client isn't without a vehicle. We have 4 techs and try to limit car count to 16 per day. While that helps, we always have "sleepovers" (cars that don't get finished and sleepover until the next day). Yesterday we had 8 sleepovers to add to our 16 that were coming in today. I feel your pain. Very often that 45 minute oil service turns into a 6 hour $1,500 repair order and we didn't have the 45 minutes to do the oil service!!
I like Newport5's suggestion of looking at deferred work when someone makes an appointment. I am going to have our front counter staff start to try to presell that def work so we have a better handle on the hours sold. I hate to push people out a week.