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Ok, just to clarify what the question is:

Suppose I am trying to decide whether to swallow an anti-aging pill which introduces some nano-bots into my bloodstream.

My doctor informs me that the bots will remove plaque from my arteries, amyloid deposits from my brain cells, and brown fat deposits from my abdomen. "Makes you look and feel ten years younger, and adds fifteen years to your life expectancy. But there are some side effects, including personality changes."

"Well doc," I answer, "the important thing to me is that I keep my sense of humor. That, more than anything else, is my VI. If the pill preserves my sense of humor, then any other changes it might make to my personality are tolerable."

"Just a second," interjects nurse HoverHell, who had been lurking nearby. "You need to define your VI physically. After all, we aren't dualists here."

"But I don't know how to define my sense of humor physically," I reply. "I define it operationally, by which TV shows I like, which jokes I laugh at, whether I come up with the snappy comeback and whether anyone smiles when I do."

"The nanobots work at the physical level," says HoverHell. "So we have to have a physical definition of 'sense of humor' in order to answer the question of whether the nanobots preserve it."

"Nonsense!" I reply. "You need an operational definition, so you can administer behavioral sense-of-humor tests to people before and after they take the pill, interview friends and families, and characterize the side-effect at the behavioral level. Claims that something is preserved (within certain tolerances) at the physical-level don't help me at all, since what I am really interested in is whether or not my sense of humor changes."

I'm not sure how the dialog proceeds from this point.

I don't think the thing I want to preserve is a physical entity so I don't think there is a way to correctly define it that way.

First there is the brain. This brain has specific input and specific output nerves. There is a relationship between input collected over time and output. This is the first thing I want to preserve. There also is a relationship between output and input. In my current situation specific output (e.g. speaking) produces a physical effect in the surrounding world that again produces specific input. This relation is the second thing I want to preserve. And third, I want to preserve the collected input over time that already determines my brain's output so that after the upload (or the like) new input is added to this collection. I think that's all.

Edit: I think number 2 is ill specified. I need to think about that some more.

I'm not sure there is anything I really want to preserve by means of personal immortality.

But assuming that there is, it's a specific dynamic pattern of relationships among representations of hypothetical attributes of my environment (including me). Which includes a number of words that I haven't defined here, admittedly.

It could be instantiated physically in any number of ways. It's (probably) currently instantiated in a network of protoplasmic cells, but I don't particularly want to preserve any part of that network.

Edit: Responding to the edited question... the direction is a more precise and detailed understanding of how cognitive structures relate to one another, and relate to events in the world.