Well, the hard part about sensory processing disorder is that every child is unique in their constellation of needs. So the trick is figuring out what are the triggers. I think with what you've said about dd, it is definitely something worth investigating. And the tantrums can be directly related to a sensory event or indirectly. In other words, imagine if there was a constant irritating buzzing in your ear (this is just a metaphor) that you successfully ignore all day long. Then towards the end of the day or week, someone like a sibling does something that frustrates you. Maybe it wasn't really that big of a deal, but it was the last straw and you just lose it. And imagine that you're only 6 years old and trying to deal with that. For me, it made my ds's behavior make more sense. For example, he would be fine most of the time in school and then almost every Thursday afternoon he would lose it and I would get a call from the school that he's being disruptive, disrespectful, etc. Now that I understand his SPD I see those meltdowns differently. And at that age, it is hard for them to express what the problem is, although, when I think back to what he would say, I realize he was telling me and I just wasn't comprehending.
A sensory diet is a set of daily activities that have a calming effect on the person. I think of them as activities that make that irritating buzzing go away or least get alot quieter. It is different for each person, so you'd have to try different things to see what helped. But it can involve swinging, trampolines, heavy lifting/pushing, weighted things like backpacks or blankets. An OT would work with you to figure out what your dd's specific needs are. And yes there are definitely things that can be done at school. Does she ever complain about being uncomfortable at school?

I also think there is significant overlap between SPD and the overexcitabilities attributed to gifties. I think it is hard to draw a clear line between the two, but since the interventions are similar it probably doesn't matter so much. But when I think of my son's intensities, his SPD seems to fit. It's like he experiences the world more intensely and therefore sometimes welcomes the experiences and wants more(the seeking) and sometimes gets overwhelmed and needs to get away from it (the avoiding). What is important is figuring out your child's specific triggers and trial and error to find what helps her. I found that asking DS about the experience not when the meltdown happens but later when he is calmer, I was able to get some insights.

The upside is that even though DS had a horrible 1st grade teacher who made him feel like a bad kid (we eventually switched classrooms and his behavior improved dramatically), in 2nd grade he has been fantastic at school and much better at home now that we have recognized and responded to the sensory issues (I also met with the teacher right away and explained some of his issues and suggestions for dealing with them, this helped alot I think!).
So it does get better!! smile