Not hatin on it at all imo
The way I like to explain five is starting with the title "A New Beginning" cause that's really what it is. Tommy had just been through some damaging psychological trauma that obviously is going to mentally and emotionally take a toll on him (which it did). That innate fear that he has to wrestle with "What If?"..ya know? what if Jason really isn't dead and is out there looking for him? Hence the hallucinations he suffers from, because of a) the trauma he just suffered and b) the underlying fear which is consuming him. So it makes perfect sense that he was admitted to a halfway house for treatment on working through said issues.
I like your explanation to 4(his death) followed by 6 (his rebirth) in regards to Jason, but def think 5 is Tommy's film. A clear cut explanation is given by Matthew from Tommy's case file as to what the overall goal is. Then from there it just plays itself out.