Heres my go. It assumes that if a quote is used as a quote it won't be surrounded on both sides by an alpha char.

$_=<<END;
  this is some text.
  A period (".") usually terminates a statement.
  But not if it's quoted.
  Regardless of whether or not single quotes, '.', are used.
END
#'  

my $accept=qr/(?:               
                (?<![a-z]) 
                (?:
                    [''] (?:[^''\\]+|\\.)* [''] 
                |
                    [""] (?:[^""\\]+|\\.)* [""] 
                )
                (?![a-z])
            |
                  [^\\''"".]+
            |
                  [''""]
            )+/xi;

  
my @parts;
  
while (/($accept|([.][\r\n]*))/gxi) 
{
    push @parts,$1 unless $2;
}
print "part1: $_\n" for @parts;
my @parts2=split / (?!$accept)([.][\r\n]*)/xi, $_;
print "---\n";            
print "part2: $_\n" for @parts;            
__END__
part1:   this is some text
part1:   A period (".") usually terminates a statement
part1:   But not if it's quoted
part1:   Regardless of whether or not single quotes, '.', are used
---
part2:   this is some text
part2:   A period (".") usually terminates a statement
part2:   But not if it's quoted
part2:   Regardless of whether or not single quotes, '.', are used
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Just in case anyone wonders, the [''] trick is harmless, perl just ignores dupes in a char class, but it keeps some syntax highlighting editors (like mine) from getting confused.