I don't think anything you do will get rapid results with laurel. Not even sure a grinder will kill it. I suggest you use SBK, applied every six weeks, but the label says a maximum of two applications per season, but I might ignore that for a stump.
The manufacturers recommend waiting for six weeks before replanting, so there must be some residue that hangs around.
TBH I wouldn't try to do anything with the area for a while. Eventually you'll have to dig out the roots to be sure of getting rid. You do NOT want a laurel growing under your shed.
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