I too am right leg dominant.
When I first got back into cycling, it took some decent concentration to get both legs to put out the same effort.
After a while, muscle memory builds up and you forget about it.
I try not to pull up too much, as it led me to an ankle injury that took a good couple months to stop bugging me.
Instead of trying to pull up, envision trying to scrape mud off the bottom of your shoe at the bottom of each pedal stroke.
It will help keep you turning to cranks smoothly in nice circles.