One possible idea would be to scope all your variables as package-scoped variables (not using 'my' at all) and then putting all your eval'ed code within another package. Something like the untested

package Foo;

$Foo::var1 = 'VAR_A';

my $pkg = '_eval_';
$Foo::var2 = <<"__END_EVAL__";
package $pkg;

print "VAR_B( \$${pkg}::var1 )\\n";
__END_EVAL__

eval $Foo::var2;
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In other words, you could, but it would be very messy and would require you to code in a completely odd style. The issue you're running into is that eval'ed code is compiled and executed within the context that the eval() call has.

More importantly - why are you wanting to do this? There most likely is a better way to do what you're trying to do ...