Utilize CTAD in the code more widely

We have some pretty gross types that we have to initialize in places, especially when it comes to the PTE solvers.

Instead of explicitly declaring these types, it may be more useful to implement [CTAD](https://en.cppreference.com/w/cpp/language/class_template_argument_deduction.html) in various places so that the class template can be automatically deduced from the constructor arguments.