On automobiles, extreme lean in corners is handled with sway bars- long steel bars that connect to the suspension at a pivot point very close to the wheels- either on a lower control arm or on a solid axle. The idea is that the suspension's independence is limited. The left control arm is limited from moving upward unless the right control arm is also moving upward. That way you get shock absorption, but in turns, it limits lean. It would seem to me that on a trike with suspension, this would be very desirable. Yes, it would add some weight, but the driveability would seem like it would go way up. Perhaps somebody who's tried a sway bar on a fully suspended trike could chime in.
This video (as sales oriented as it is) is quite good:
This video (as sales oriented as it is) is quite good: