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Head to a corporate Verizon store (as suggested elsewhere), get a new SIM from them for free, have them activate it on your new phone.
If that doesn't work:
Get a SIM Adapter Tool, get a new Verizon nano-SIM from above, activate it on your Note 4 using the microSIM adapter, then put it in your Note 8 and profit
I've used a Verizon Note 4 and unlocked Note 8 (currently a Canadian Note 8 with US Unlocked firmware) on Verizon, using method #2, and still using the same number.
If you can purchase through US based Amazon, this might work for you: