"a variety of different constructors"? I may be a newcomer to OOP, but that's a recipe for disaster unless you factor out the commonalities at the package level and create private methods that do those parts for your various public constructors.
Another solution, if you absolutely insist on a myriad of monolithic constructor routines (again, these sound like a maintenance nightmare), is to create a package global that holds a default $self to be assigned when you declare my $self the first time in each constructor, and then over-ridden as the parameters are dealt with.