Simple and efficient solution:

Make one class superclass of all your othe classes. Let's call it My::Object. All your other classes will inherit from it. Place every method, that sould be 'universaly inherited' in this superclass. If you need 'global' variables, make them static variables of class My::Object. It looks like this:

package My::Object;

use vars qw($global1 $global2);

sub global1 { $global1 }
sub global2 { $global2 }

sub globalMethod { ... }

package My::SomeClass;

use base qw(My::Object);

package main;

my $g1 = My::Object->global1;

$any_my_object->globalMethod();
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Note1: It is VERY bad to mess up with 'magic' classes like UNIVERSAL is. Not because it won't work, but because it will look bad. And if it will look bad, it will be unreadable. Thik about hubris. A year after you write it you will not be able to understand how it works.

Note2: Avoid 'global' and even 'class static' variables whenever you can. They will make your life a real pain in long-term development. Every one of them. Use of global variable of any kind can be avoided by careful object design of application. As you are rewriting your application, you should be aware of how it works, so good desing sould be your primary aim here.