Firstly, don't assume that perl will assign either of those values correctly. At around those precisions, it's not uncommon for perl to assign values that are off by (up to) a few ULPs.

I would do it with Math::MPFR (though the real credit goes to the mpfr library):

use strict;
use warnings;
use Math::MPFR qw(:mpfr);

# Set $prec and $out_prec appropriately

my $prec = 53;   # NV has 53-bit significand
# my $prec = 64; # NV has 64-bit significand
# my $prec = 106; # NV has 106-bit significand
# my $prec = 113; # NV has 113-bit significand

Rmpfr_set_default_prec($prec);

my $str1 = '1.9041105342991877e+258';
my $str2 = '-8.2727285363069939e-293';

my $obj1 = Math::MPFR->new($str1);
my $obj2 = Math::MPFR->new($str2);

Rmpfr_nextbelow($obj1);
Rmpfr_nextabove($obj2);

print "$obj1\n$obj2\n";

# To convert the objects to NVs:

my $nv1 = Rmpfr_get_NV($obj1, MPFR_RNDN);
my $nv2 = Rmpfr_get_NV($obj2, MPFR_RNDN);

my $out_prec = 17;   # 53-bit significand
# my $out_prec = 21; # 64-bit significand
# my $out_prec = 33; # 106-bit significand
# my $out_prec = 36; # 113-bit significand

$out_prec--;

printf "%.${out_prec}e\n%.${out_prec}e\n", $nv1, $nv2;

__END__
Outputs:
1.9041105342991875e258
-8.2727285363069927e-293
1.9041105342991875e+258
-8.2727285363069927e-293
[download]

To put it glibly, we just need to increase/decrease the value by one ULP.

Cheers,
Rob