DFT vs. MP2 for stacked dimer
Both papers you refer to used methods which were basically state of the art at their time (Gaussian 98/03 compared to Gaussian 16 today). But that is almost twenty (or fifteen) years ago. Nowadays we thankfully have more developed methods available, and one should check whether the results found back then are still consistent. An (admittedly also a bit outdated) overview can be found here: DFT Functional Selection Criteria.

Long story short: You cannot reliably perform calculations on complexes where non-covalent interactions are dominant. You need to to use a method that treats dispersion at least at an empirically derived level. A popular example is Grimmes DFT-D3 program, which is also available in many ESS codes. (Starting point is The Journal of Chemical Physics 2010, 132 (15), 154104.) In the semi-empirical method xtb a newer version is already implemented.

For that reason I guess (since I only read the methods sections) they used MP2 for molecular structure optimisations, as it recovers dispersion interactions to some degree.

Whether or not DFT is suitable for your investigations, I cannot say. A thorough research of the recent literature will certainly offer far better insight.

The Pople basis sets, while an excellent example to understand the structure of them, are generally a terrible choice for almost everything practical. There are multiple basis sets available, which produce more consistent results, and are better optimised to perform in modern ESS codes. If implementations are missing from you ESS program of choice, you have a high chance to find it in the Basis Set Exchange Library.

For ORCA there are most (if not all) Ahlrichs' def2-variations are available, see the ORCA input library.
I would expect augmented basis sets (ma-def2-XVP or def2-XVPD) are necessary to investigate such complexes.