We did something similar at a mates place, but him being smart and lazy made him think about how to, a bit too much first. He basicly did exactly as you have but he added a threaded hole (M10) in the centre as well. He then got a length of M10 rod and dropped it in through the locker and wound the base plate up with a drill on the end of the thread passing though the plate. Once everything was in place and fitted he removed the rod. One thing he did do differently was to make each of the bolts from underneath a slightly different length. That way as it came up he could line them up one at a time rather than all four at once.
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