However, I can't seem to figure out how to get my BSV. I tried importing my original BTC private keys into the ElectrumSV, but it's showing a zero balance.
You've got it wrong, Bitcoin SV isn't a fork of bitcoin but it's a fork of Bitcoin Cash ABC also known as BCH.
I've tried the Atomic Wallet, but it apparently doesn't support importing private keys. I'm assuming I should be importing the original BTC wallet keys.
Nope, you should import the bitcoin cash wallet key not the original bitcoin.
Check this guide:
How to Claim free BCH-SV forked coin and How to Exchange into Bitcoin?