#<====== Note the ; " ; at the end. This seems required.

No, only the second semicolon is required. And why wouldn't it be? Statements generally need semicolons to separate them from the next statement, apart from block-like statements like if ($cond} { BLOCK } which don't need a semicolon after.

The difference between the two eval uses can be summed up like this:

use strict;
use warnings;
use feature 'say';

my $var = "Hello";

eval " say '$var' ";

eval { say '$var' };
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If you understand why those two have different results, you will understand why stringy eval is working for you and block eval is not.

Understanding why this works but you couldn't do it with the block form of eval might also help:

use strict;
use warnings;

my $var = q(Hello',"\n");

eval "print '$var";
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