Your question about time to pod production from regrowth may be something that you just have to experiment with to figure out yourself. But in general a mesquite tree will begin to produce pods 3 years after planting but it may take 4 or more years to reach full production.
As far as I know a mesquite will grow back from the base if completely cut and will form a thicker shrubbier plant. I don't know how many times you can do this to a mesquite though. Pruning the tree branch by branch as you say that you would like to do on a yearly rotation sounds like a great idea to me. At the World Hunger Relief Farm in Waco leucaena is used in a similar matter in some
perennial beds. The prunings can be used as mulch to add more nutrients and nitrogen, and the nitrogen contained in the root-mycorrhizal association beneath the tree are released. According to
Bill Mollison there are specific
roots directly in relation with specific branches above the tree. Thus when pruning leguminous trees (farmer's trees) a corresponding root will give a sudden release of nitrogen to the plants around it.
In addition to the nitrogen fixing abilities the Mesquites have wide lateral roots which accumulate nutrients from the surrounding soil and deposit the nutrients directly under the tree. Mesquite has been shown to increase N,K,S, Soluble salts, and organic matter directly under the
canopy.
The mesquite trees are naturally smaller and provide a nice dappled shade for many plants and does act as a nurse plant in natural environments. I don't know where you are but I am assuming that you live in an arid or semi arid area and it is probably hot. I live in Central Texas and there are many
honey mesquites here. Current research has shown that in Texas the sun is so intense that even plants that conventionally are supposed to get full sun actually do better with some shade. This is because there is a cap to a plants photosynthesis capabilities and so after a certain point the plant just can't utilize any for sunlight. So this may just be another bonus depending on where you live.
I plan to implement a similar production system as what you are describing. I recently harvested 150 lbs of honey mesquite pods. Mesquite bread is amazing. I am really looking forward to roasting some of the pods to make some mesquite
coffee.
Cheers!