This presumes that there is something special in this model that doesn’t resume when your mind resumes running in it’s new location. Or, in other terms, “a soul”.

That is ridiculous.

So you do see my point.

People aren't computers, so getting all worked up about how software models instances still isn't a valid modelling for human consciousness.

When you kill a process and you re-run a program, even if you saved the full state of the memory elsewhere, you don’t say that it’s the same process. Is another process with identical content. There’s no need of a metaphysical entity. It’s another instance.

But this is so hair-splittingly pedantic it's almost doubled back to be incorrect. If you ask 99.999% of the world, they'll be like "yeah I closed outlook and then I opened outlook" - to them, it's still the same program. They're launching the same software again. No one is like "oh well once you quit Skyrim it's all over because even if you reopen it later, it's a new instance and the old one is dead" ... no. That's ridiculous. It's the same program, the same save file, resumed from save at a later date.

Your focus on "Process" instead of "Program" is making the soul argument. The "process" you're arguing for is a soul. Something intangible and irrelevant to the end user, that does get terminated on shutdown, that cannot be restored from save. Consciousness is the software, not the process itself. Memories are the save file. There is nothing in OP's model of teleporting that suggests "process" itself is the sacred portion - when the hardware & software of "Dave" gets paused and resumed flawlessly.

You’re deeply, sorely mistaken. Even in a deep, unconscious state, the mind keeps working, even if the degree of consciousness is different. That we’re not 100% certain of what the brain does in those moments doesn’t mean that it stops working.

Not at all. Consciousness is interrupted. Unless we're assuming that the "process" itself is sacred - what happens to consciousness is all that matters in either case. If your ability to perceive yourself as a conscious being stops - it doesn't matter to your experience of your own consciousness if the 'process' stopped or went to sleep during the gap.