You need to
    use Data::Dumper;
in order for the  Dumper function to be accessible in your code; then
    print Dumper $sheet;
will actually print something. See Data::Dumper. (I tend to like Data::Dump a bit better.)

... even though I have:
$sheet = $book->[$sheet_index] or next;
this does not seem to be doing the trick.

But my point remains the same: in order for a statement like
    $name = $sheet{"${_}28"};
to work, a hash named  %sheet must exist somewhere in your code (somewhere in scope, that is). I.e., there must be a statement something like
    my %sheet = ( ... );
somewhere. Do you say that such a statement exists?

Update: The other point to make is that if the  %sheet hash actually does exist, the expressions  $sheet{"F28"} and  $sheet->{"F28"} access two completely different hashes!