Answer: I admire your willingness to get out into the yard and make it beautiful. For starters, you are dealing with extremely alkaline soils which will dictate the types of plants you will be successful with. You probably cannot change the slope of the soil without disrupting the drainage so perhaps you might consider gardening in raised beds. Raised beds can be filled with amended soils and provide more hospitable growing spaces for the roots of your plants. If you choose not to install raised beds, try planting shallow-rooted plants so the roots do not have to deal with growing in calache (the soil type prevalent in the desert southwest).
It can be difficult to get things to grow under pine trees. They cast dense shade, their fibrous roots are shallow and will compete with the roots of other plants for moisture, and they drop needles which can acidify the soil. I'd recommend leaving the earth beneath the pine bare, or planting it with a shade-tolerant, acid loving groundcover such as vinca minor.
I suspect that the dead zone you describe has a lot to do with the acidity from the pine tree. Your bougainvilleas grow best in alkaline soils and the excess acidity from the pine has affected the one.
Bougainvilleas can be pruned at most any time of year in your growing region. I'd prune it back now so when the weather warms it will put out a new flush of growth. Transplanting can be done now, too. The recent rains should make digging easy and with more rain in the forecast, the newly transplanted shrubs should root readily.
Best wishes with your landscape!
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