Before going further find out what soil and surcharge pressures the wall is designed for, such as at-rest, active or passive and of course then the loads on the wall as a result. Then, you can compute loads into any bracing. If you don't follow my advice as to a loose zone left next to the wall, you must then assume conservative loadings in excess of passive pressure loadings due to that compaction work. Lacking any input from designer, I'd double the passive pressure loadings for the temporary bracing. For ordinary earth backfill this could be as high as 600 pcf equivalent fluid, certainly at least 300 pcf. How much pressure remains after the backfilling is done also needs to be known Then be sure the designer knows that question is still there. After that step, you can design the bracing.
As to type of bracing, others here may have advice. Be sure to consider the forces on the supports for your bracing and the allowable lateral earth pressure there. It is not the same as for vertical loads, very likely.
The assumed cost saving using the reinforced masonry may well not be there because of all the grief of holding the wall when filling behind it. Reconsidering the overall design might change this whole affair.
I would hope my use of the word "backfilling" is not confusing, because it really is just "filling". Force of habit.