Recipes for sugar scrubs can be so confusing, because there are so many variations:
~emulsified v. non-emulsified
~foaming v. non-foaming
~paste v. cubes v. piped shapes v. rolled, etc.
An emulsifier helps the oils in the scrub to disperse across your skin, and for the oil that hit the floor, to wash down the drain, rather than leaving your floor oily and slick. For that reason alone, I really prefer emulsified scrubs.
The recipe that I prefer for foaming sugar scrub cubes is from DIY Bath & Body (of course, lol). It is one of the free recipes on her FB page if you join that group. It does have a few more ingredients than yours, including
Mandala scrubs that add a unique touch to the blend, including SLSa to add foaming and cleansing properties in addition to what is provided by some M&P base. It also uses a foaming bath butter base, but you may be able to adjust the amount of M&P base instead.