I am happy to help out! I understand what you are looking for and why it is so important. However, there currently is no practical way to override the level-of-details settings for all visible tiles in the Cesium viewer.
Did you end up trying a variety of data sources as I suggested? I suspect that this is the best temporary workaround. I am curious to hear how this will impact your application. For instance, the ESRI World Imagery seems to meet your needs.
As you can see, all tiles appear to have a similar level of detail. We also are not seeing any harsh imagery cutoffs.
What exactly do you mean by caching the tiles? It is unclear to me what your implementation would look like with this idea.
Let me know if you have any other questions or concerns. It looks like the last part of your reply was cut off. I am looking forward to learning more about your application!