Washingtonias do not need heat to thrive (they do great in our climate, which is extremely mild, cooler than yours in the summer) and they are not at all demanding about nutrients (they grow in nearly pure alluvial sand both in nature and in various places around here).
You will likely get good results from that plant by keeping the amount limited. Measure what you use. Start low, observe growth, and go up as needed. If you have a lot of plants, do an experiment with two groups treated differently, which ought to be informative.
I would dissolve the product in water before application in order to avoid toxicity issues and ensure a more even distribution. You will get better results (all things equal) with repeat application at a lower level, if that is possible, because of the soil limitations you have described (nutrients being constantly leached by water). And never underestimate the value of compost, even applied intermittently in the form of mulch (though ideally mixed into the soil) for giving rocky soil long term potential.
I do not know much about boron but it may actually be the most hazardous component of the mix when delivered in excess. There is a relatively small difference between a therapeutic dose and one that limits growth. You can read up on this if it concerns you.
