I think it will work better if you set the same duty cycle for all the converters. Stagger the timing cycles 120 degrees apart. Any time you adjust the duty cycle, apply it to all the converters.
Reason: From your description, you believe each inductor should carry equal current, so you have each converter operating independently of the other two. However when you make a change in one converter, it affects action in another converter. The control modules will tend to 'jostle about', and your output will be less-than-stable. Or, it will need a long settling time after you make some change.
In case it will help to look at some simulated scope traces, I got out my virtual triple interleaved boost converter. The timing cycles are equal.
I set one inductor to an oddball value (25% high). Notice that inductor carries greater Amperes, but the variation is not as severe as we would be led to expect.
In fact, it is the coil's DC resistance, which is more likely to create differences in behavior.