... [I] don't need "secure" randomness, I just need files with a specific size ...

The general tone of your posts and the fact that you were comfortable with the 3115-bit built-in rand in the first place leads one to imagine that you might be satisfied with data having the first-glance appearance of randomness. The following is quite fast: well under a second by an eyeball timing on my laptop. I didn't try to fill up my HD (I don't have a SSD), but even so...

>perl -wMstrict -e
"use List::Util qw(shuffle);
 ;;
 my @chars = ('a'..'z', 'A'..'Z', '0'..'9', qw[- _ ! & ? =]);
 @chars = (@chars) x 100;
 my $jumble = join '', shuffle @chars;
 $jumble .= reverse $jumble;
 ;;
 use constant MAX => 10 * 1024 * 1024;
 ;;
 my $j_len = length $jumble;
 die 'wrong assumptions' unless $j_len < MAX;
 ;;
 open my $fh, '>', 'faux-rand' or die qq{opening: $!};
 print $fh $jumble or die qq{writing: $!} for 1 .. int(MAX / $j_len);
 my $shortfall = MAX % $j_len;
 print $fh substr($jumble, 0, $shortfall) or die qq{writing: $!};
 close $fh or die qq{closing: $!};
"
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