Well, about the earliest anyone that I know will bake a cake that is due for a Saturday, is about the Wednesday before. What you have to remember is that the cake even in that case will be 3 days old. Plus if people have leftovers they will want to be able to keep them for a couple of days.
I understand that sometimes things aren't avoidable, but it isn't a good habit to get into. Generally unless a cake is realy huge, the cake should only be baked a day or two before the delivery date or frozen if the timeframe is longer. The cake if baked tomorrow will likely still be fine on Sunday though. But that is about the limit I would ever go, instead preferring to generally bake a Saturday wedding cake on the thursday before.
Filling with a pudding, well a cooked thick type of pudding filling will hold up best. Generally for cooked puddings I only fill them the day before the delivery date at the earliest. Some pudding fillings keep better than others, some reabsorb back into the cake. Puddings, being made up of milk mainly, should generally be refridgerated. So the transport method should be in an air-conditioned car and not for a long period of time and not in sunlight. It should be immediately tranferred to a refridgerator. I wouldn't travel with a cake like this for anymore than 1 hour. I take it you are filling the cake on the Thursday. That is a lot longer than I would go with a filled cake. Especially one that will be transported and one you have no control over the temperatures it is exposed to.
I find that people are doing things and saying that it worked fine. Sometimes it does and sometimes it doesn't. The thing is there are risks involved and different climatic exposures and such. Some people don't get sick from anything, others get food poisoning quite easily - diabetics, small children and the elderly.
Personally, I would not serve a cake more than 4 days old to anyone but my family and usually would throw out a cake of more than 4 days old. I would not sell a cake that was prepared more than 3 days in advance, it just isn't fresh.
I think folks need to be very careful when they are selling to the public. I think this is a huge risk for those of you in the U.S.A. where people can and will sue for almost anything.
I find that people are taking a lot of chances with the types of icings and fillings they are exposing to outdoor elements. I think the problem is that though people take decorating course, they have limited knowledge of safe baking proceedures, food safety practices and the limitations of shelf life on various ingredients.
I think that people should not take orders where time constraints will mean that the customer will be receiving a product that is deemed less than fresh.
Personally if I was in this situation, I would not use a pudding filling of any kind.
Here is a standard Simple Syrup recipe.
1 cup sugar
2/3 cup water
1/4 teaspoon cream of tartar (optional)
Servings: About 1 cup
Procedure: Combine ingredients in a small saucepan. Cook, stirring gently with a wooden spoon over low heat until the mixture is hot to the touch and most of the sugar is dissolved; do not stir again, or the sugar may crystallize as it cools. Brush down the insides of the pan with a wet pastry brush and bring to a simmer. Cover and simmer gently for 2 minutes. Remove from heat and let cool, uncovered, before using.
Storage: This keeps in a covered container for up to three weeks at room temperature, or up to 6 months refrigerated. Use it to sweeten coldor alcoholic drinks, or to combine with liqueurs to moisten cake layers before filling and frosting.
You may add 1-2 tbsp. of a liquer to use as a flavouring.