3/4" nailed down hardwood will bridge 16"----In the old days hardwood flooring was nailed to 1x2 sleepers space 16" on centers----this allowed the electrician to run conduit between the subfloor and the hardwood.
If you have some gaps,you will be fine.
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I personally wouldn't worry to much about squareness. Most of the time, squareness problems occur at a wall/floor joint. Most people do not walk on the floor next to a wall. make sure that you lay the hardwood across the floor joists as opposed to parallel to the floor joists.