That's an interesting idea! However, I am not sure how to sustain such a "La Nina Effect" in the face of the energy imbalance caused by increasing greenhouse gases. El Nino and La Nina cause large fluctuations in sea level and global mean temperature, but they do not cause long-term changes in the amount of energy entering and leaving earth's atmosphere. So, in the long run, they have no effect on the global temperatures or sea level.

Increasing greenhouse gases, on the other hand, cause an energy imbalance that continuously increases the ocean heat content (raising sea levels) and surface temperature. So, any long-term solution would need to oppose this energy imbalance or modify the carbon cycle substantially. I am not sure how such a geoengineering feat involving La Nina-like effects could do that, but I haven't thought about this that deeply.