So I found a solution that approximates my desired behavior. In the admin panel, go to Extend > Rewards. Create a new reward with the following rules
If User's: Post Count
Is: > 0
Then: Award Reputation
Amount of reputation: 1
This will add 1 reputation for a user on every post, but each post will still start with 0 votes.
I had a bit of a play with it.... Works as advertised... Great plugin.
I'd love the ability to share a copy of the assets folder somehow as well tho. But I know this wouldn't be very safe.