To gauge how well these languages have achieved their goals, we really need to quantify what exactly achieving those goals would entail, and what steps along that path we would consider progress. What constitutes success for Toki Pona or Loglan? A world of people thinking differently? A small group of speakers who have improved the way they think substantially based on learning the language? Without knowing that, we cannot say whether these languages have achieved their goals.
Additionally, when looking for research into linguistic relativity, the place to look would be linguistic research, and we're unlikely to see much research into Toki Pona's or Loglan's influence on the minds of their speakers. Why? Well, strong Sapir-Whorf is pretty much a settled question in linguistics -- the vast majority of the field agrees it's not the case -- and weak Sapir-Whorf is more likely to be tested on natlangs for many reasons, not least of which is the number of potential subjects. Even the most popular conlangs have much smaller speaker communities compared to most natlangs, and so even if conlangs and natlangs were equal in all other ways when it came to this research (and from a linguist's perspective, they really aren't), it would be far harder to gather subjects and conduct research for the conlangs.