La Mulana and Banjo Kazooie have entirely different types of secrets. With very, very few exceptions BK uses solely lock-key (each solution only solves one puzzle and each puzzle requires only one solution) puzzles and ability puzzles; in contrast, La Mulana has these in addition to research puzzles, which have multiple solutions required for their completion, such as the wedge puzzle requiring the knowledge of multiple tablets and the manual, or fighting the shoot-em-up boss requiring the ankh jewel, finding the ankh, and using the key to start the vehicle. Banjo Tooie experimented with a few research puzzles, such as the train jiggy in HFP, but in my eyes these failed for the same reason most boss fights did in the game- having a universal reward, a jiggy, means that only players going for 100% will go for these more complex puzzles. The only ways for La Mulana puzzles to work in a collectathon are for them to either reward multiple of the collectible (such as how the first challenge on SM in N&B rewards six jiggies), be required for fighting the final boss, or reward something entirely different, such as a new ability.
DLC? UGANDA WILL NOT HAVE THIS SICKNESS!