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Another path to pursue is to change the apparatus and use tubes with a bigger diameter, allowing for the increase of upflow velocity and to experiment with a higher amount of lime. This would also let the water flow in the vertical direction and avoid the fast expulsion of lime.
2. Change of apparatus design:
Another option is to develop a completely new design. As a suggestion, there is a lime feeder design described in the book "Surface Water Treatment for Communities in Developing Countries" by Schultz and Okun, 1992. According to the authors, this apparatus was used in a water treatment plant in Brazil. The design does not involve electricity, just hydraulic considerations.
Figure 1. Brazilian design
Figure created by ChengFeng Wu, based on the referenced book