I've modulated lasers with RF by setting the DC current half-way between the threashold and maximum. In your case the difference betweeen threshold and maximum current is 110-20=90 mA, so set the current at 20 + 90/2 = 20 + 45 = 65 mA. Then you can get close to 100% modulation depth using a peak current of 45 mA, which is an RMS current of 32 mA.
I'm a bit confused by some of what you wrote, but if you bias it at 40 mA as I think you are implying, and have 20 mA RMS current for modulation, then the peak modulation current is going to be 28 mA, so the current would attempt to drop to 40-28=12 mA and so be below threshold.
Be careful if running lasers at their maximum current. They make extreamly fast fuses. You need to ensure there are no transients on your power supply.