How to Work on Increasing Tempo

Hi
I’ve completed and memorized Moon River and Autumn Leaves from the Lead Sheet Fundamentals learning path and now just starting on Misty. I learned both of these songs at a very slow tempo/rubato technique to get a better understanding and feel of the 251 progressions and seeing how the 7ths drop to 3rds. These lessons have really helped me a lot.
Now I’m trying to increase the tempo by playing with a metronome but the straight feel is making it difficult to play with a rubato/ballad touch. Any suggestions on how to work on increasing tempo?
All suggestions and feedback appreciated.