Difficult to comment without knowing what one of your .conf files looks like.
One possibility is to use 'do' rather than 'require', and import each one into a different namespace. For example:
/tmp/foo.conf:
sub f { print __PACKAGE__, "\n" }
1;
main script:
package P1;
do '/tmp/foo.conf';
package P2;
do '/tmp/foo.conf';
P1::f();
P2::f();
which outputs:
P1
P2