After putting the yummy stuff into your mouth, it (the bolus) then has to travel through the entire gastrointestinal tract before coming out the other end. The gastrointestinal tract for the purposes of this exercise includes the oral cavity, the oesophagus, stomach, small intestine, and colon.
Food travels down the oesophagus at a rate of approximately 3 to 4 centimetres per second (1 to 2 inches), and the entire process takes about 5 to 6 seconds. In thestomach, food tends to hang around for a little longer and this depends on a variety of factors including the amount of food you have consumed, how much fat it contains, and also the acidity of the stomach. However, all food should have left the stomach within 2 to 4 hours.
In the small intestine, digestion continues and absorption occurs. From here on, the time to defecation will vary depending on the time it takes to adequately digest and absorb in the small intestine. This will usually take 5 to 6 hours. The "food then enters the colon for further digestion and water reabsorption before defecation. The time from it’s entering the colon to defecation is about 12 to 24 hours.
Thus, the time for food to travel from one end to the other probably ranges from about 20 to 30 hours. Although I haven’t had the time to look further into the rest of your question, I hazard a guess that it is unlikely that meat will hang around for a week given that the gastrointestinal tract is very effective in breaking it down with various enzymes and acidity of the stomach. Foods high in protein and fats probably would probably take a little longer to pass through than if it were carbohydrate.