Hello @jgikegami and welcome to the BAKERforum!
An important part of product development is the research, and that usually means asking questions. My first question for you is to understand your goal. Is it to sell more apple sauce in another format or product innovation? As you are naming this Apple Carrot, perhaps you should consider increasing the Apple and reducing the carrot?
At first glance I would say the recipe looks more a pudding than a cake. Do you whip the eggs to make them light and creamy? Can you give some information in general about the process?
50 minutes seems like a very long bake time for a cake. You mentioned that you think the cake is dense. How dense is it? Have you calculated the grams per cubic centimeter?
Preserving in more than just pH and aW. Cleanliness and minimizing contact points after the kill step are also important. A pH below 4.0 is considered beneficial in reducing the opportunity for bacterial growth. Free water is important for bacteria and microbial growth. At a bare minimum 0.63 aW is considered the goal to limit growth. Most dry cookies etc. target 0.60 aW.
The idea of cake in a can is a new concept to me and sounds rather interesting. The pasteurization temperature and times seem pretty reasonable to me. Once you seal the can I would think that you create a vacuum and that in itself would provide preservation. Have you attempted a test of this at all?
I noticed you equated an egg at 67g. That seems rather large to me. On average a large egg in North America and Europe is considered 50g. How did you come up with 67g? Do you have a typo in your recipe for the eggs, should this read 3dL (300ml) instead of 3L (3,000ml)?
do you plan to bake the cake in the can and then seal it, or bake the cake, then transfer in to a can to seal?
i hope we can help you achieve your goals!