Isolate before apply.
It really is about isolating. I know that "do lots of suburi" is the old-school recommendation, but honestly, I think it's one of those pieces of received and unexamined "wisdom" that's worth questioning. If "lots of suburi" ever does have the effect of better form, it's only by doing it the dumb way, and there are lots of pitfalls along the way. Do it the smart way. Rather than doing "lots of suburi" in the hope of tiring out the big muscles enough so that they can't work any more, so that the small muscles will come into play (and will magically not become injured after having been ignored for so long), learn to isolate the small muscles from the beginning. One suggestion I use is to tell people to lift the sword with their pectoral muscles rather than arms and shoulders -- that's not exactly right either, but it gets you closer to the real thing.