I've been staring at this unholy construct $self->{&{\&{$testname}}}->($system); for about 15 minutes, And I still haven't a clue what it's meant to do.

Perhaps you could fill in the blanks?

1. $testname is a string containing the name of a subroutine?
2. \&{ $testname }; returns a code reference to the named subroutine.
3. &{ \&{ $testname } } invokes that coderef. Ie, a long winded and obfuscated way of doing: &$testname
4. $self->{ &{ \&{ $testname } } } Uses the (if any) return code from the subroutine as a key into the object hash.
5. $self->{ &{ \&{ $testname } } }->( ... ); who's associated value is another coderef, which it invokes ...
6. $self->{ &{ \&{ $testname } } }->( $system ); passing one variable $system (which is apparently a hashref.)

Unless you have pre-populated the object hash with a key matching every possible return value from every possible test name, and associated an appropriate coderef for all of those keys; that line isn't trying to do what you think it is. (And even if it is, the way it is written is unnecessarily complicated and obfuscate.)

(And a brief glance at the rest of your code makes me think you're writing code you will not be able to maintain.)