The lettering is common block lettering. While it may have been taught in Jersey schools, that is only becuase it is a common style. The spelling errors are just spelling errors. It is reading too much into them to say they come from Hooked on Phonics.
Back when I was a teacher I worked with "difficult" and troubled adolescents. The handwriting is consistent with a very depressed and intense 11 to 14 year old male. (It also could be that of an adult whose development was arrested by a traumatic event during those years.) The writing also looks to me as if it were written on the bus.
You were a teacher. It is a human tendency to interpret things in light of our experience. You see badly done block lettering and think student, because that is what you know. In reality anyone can write this way. Seeing a depressed and intense 11 to 14 year old male is reading too much into the data. That is only one way to explain it and there are many more possibilities than that.
You used the key words, "it is consistent with..." There are many things it can be consistent with. It could be consistent with 100 different scenarios.
Teaching ZIP+4 has become part of the curriculum. American adults still tend to address handwritten letters without the +4. I would also be looking for a school that had some sort of project to write to Congress; could be the address came from a school prepared list for students.
Again, that is not the only way to get the address. It isn't exclusionary. Nothing says that is THE way they got it. If one wanted to make sure the letter got to the right place one might make the effort to get the ZIP+4 right too. This is reading way too much into the data.