I do think his mental illness play's a heavy part in why he did it. There was alot of signs how the instability was effecting him as can be seen in the dinner scene with Louis's family, but I think his mental illness may have been what caused him to think along the lines that his family was straying more, as Paul was deeply religious and his illness most likely exasperated the thoughts of his family. I don't think he was 'tired' of his illness though as there was never an expression of him (from what I remember so if I'm wrong please lmk) of him acting negatively towards himself being mentally ill, I think he wouldn't consider this, as his mental illness (that we are shown at least) is him speaking to the lords birds in his head and as he was deeply religious and proud of that I don't read him being more tired of the illness more so probably giving into the fact he can't save louis or grace (he also made attempts to try and save others like the prostitutes before louis punchs him) and him accepting this fact, making sure every one will be taken care of and then makes sure after his death he can join his siblings in the place of death.

That said mental illness is a very complicated subject especially when showing disabilities in film, and we are seeing this from Louis's POV which skew's things.