#!/usr/bin/perl

local $/ = undef;
my $string = <DATA>;

$string =~ s/^(Heading Here:)$/\n$1/m;
while ( $string =~ s/^(Heading Here:.*\n)(\S.+)(\nAnother Heading:)$/$1  $2$3/gsm ) {}
while ( $string =~ s/^(Another Heading:.*\n)(\S.+)(\nEnd of section:)/$1  $2$3/gsm ) {}

print $string;

__DATA__
Key: Value
Item:
Another Item: Text
Etc Etc: Whatever
Heading Here:
Indent This: Stuff
By 2 spaces:
Every line: Until
The Next: Heading
Efficiently: If possible
Another Heading:
More:
Stuff:
To: Indent
End of section: Stop indenting
Random: Test
There: Is more stuff
Further down: The string

##</code><code>##

Key: Value
Item:
Another Item: Text
Etc Etc: Whatever

Heading Here:
  Indent This: Stuff
  By 2 spaces:
  Every line: Until
  The Next: Heading
  Efficiently: If possible
Another Heading:
  More:
  Stuff:
  To: Indent
End of section: Stop indenting
Random: Test
There: Is more stuff
Further down: The string