There is another possibility as to how the Romulans aquired the Klingon Battlecruiser, as a war prize after a border skirmish?
JDW
That's the funny thing about "The Enterprise Incident": somehow people assumed when they saw Romulans using Klingon ships and Spock said "Intelligence reports Romulans now using Klingon design", that the Romulans and the Klingons must be allies. That doesn't necessarily follow.
It could be that the Romulans stole the Klingon design, or acquired peices of it from a third party, or salvaged a wrecked Klingon ship and reverse-engineered, etc. I never understood what would motivate the Romulans and Klingons to work together.