I once made this point to a believing Christian and it confused her just as a JW would be confused if they heard it. It's as if she made herself oblivious to what I had just said and then she began expressing her spiritual beliefs.
exJW
Here's the Hebrew word מוּת - die (as translated in the passage)
Strong’s Definitions מוּת mûwth, mooth; a primitive root; to die (literally or figuratively); causatively, to kill:—× at all, × crying, (be) dead (body, man, one), (put to, worthy of) death, destroy(-er), (cause to, be like to, must) die, kill, necro(-mancer), × must needs, slay, × surely, × very suddenly, × in (no) wise.
So.. Why is your interpretation correct?
The Hebrew is, literally, die-die (muwth-muwth) with two different verb tenses (dying and die), which can be translated as “surely die” or “dying you shall die.” This indicates the beginning of dying, an ingressive sense, which finally culminates with death.
I'm responding specifically to the JW doctrine. You bring up good points for anyone who wants to dig in deeper.
The thing with stuff like this is that the people most obsessed with them will always find a way to distort it to maintain their views and beliefs.
"Oh he meant it like in a spiritual death, because them Adam and Eve were cut off from His grace when they were expelled from paradise" or whatever