Hmmm... so since these bare trunked trees are deciduous conifers they are likely bald-cypress. This tree can go to over 100 feet tall when given room, but close planted here they will continue to do exactly what you don't want, lose lower branches. These trees were clearly the wrong species to plant in that location; perhaps they were a low cost alternative when very young and suitable as a stop gap measure. Now, realistically speaking the only way forward is complete removal of the line of trees, refresh of the soil and replant with a species for your area that has more restricted height and is suitable as hedging, that is tolerates close planting without losing lower branches.
Planting underneath the existing trees would be impractical. The soil is probably quite depleted. Light is frequently a problem for underplanting but as the lower branches die off the light will increase. It's the soil that is the problem. Plastic fencing would not be worried about soil quality. But the trees will continue to be a problem waiting to be taken care of.