A good ratio and timed finishes will set the boat. I always try to get people to stop working on handle height for set since in a majority of cases this just creates tension and that's the #1 enemy when it comes to balance.
In a very good crew, ratio comes from quickly picking up the pressure at the catch and accelerating all the way through to the finish, regardless of the rate. When you're having big issues, I would use the following progression to get better:
1. Learn to sit on your butt. Sounds really stupid but most rowers actually fail to do this. The "gathering point" is at bodies-over position: arms fully extended, all the reach forward you're going to get from the hips and legs straight. Learn to relax at this point. Just sit in the boat; only the core is engaged at this time so that your back is in a strong position for the catch. Bodies-over pause drills are the staple exercise to learn this; rowing with people sitting out if necessary to keep the balance.
2. Use proper sequencing during the drive. Hang as long as you can, only using the legs and engaging the core. Then open the back and finally pull in the arms. Legs only drills are great here since they also re-enforce proper body prep. Most crews would need to do these with people sitting out at first.
3. Accelerate each stroke. And I mean each stroke. When the intensity is low, the rate should be lowered rather than dropping pressure to zero. A good crew never, never, never rows without continuous acceleration from catch to finish. We have the pleasure of watching the National team almost every day and this is what they do. In order to be able to accelerate, you have to feel the difference between pushing the boat forward and ripping the blade through the water. Strokes from a dead stop are good to experience this. Another thing to remember is to be patient and relax. You have a lot more time at the front end than you think. The relaxation and body prep helps to feel the pick-up at the catch.
4. Slide control. If you're body prep is good, this becomes much easier to do. When you start to feel acceleration through the drive and proper slide control, you row with ratio. Remember, though, that acceleration is more important than slide control. In the end, contrary to what many people are saying, most of the difference in movement speeds in going to higher rates lies in the recovery. So a crew that rows a high rate is faster on the slide. However, in order to use the high rate effectively, the slide speed needs to be "justified" by length and acceleration on the drive, which become much harder at high rates (not too mention much more tiresome).
5. Finishing together. It will improve naturally for most crews with the above, but it's the final step to set the boat. Rowing square blades or quarter feather, if possible without people sitting out, helps to get the timing and proper tap-down height.
It takes most people a few years to learn all this but once you experience the feeling of great ratio, it never goes away. Good luck!