the problem is that you only have 5 inches soil. the roots are hitting plastic and when you water they are just sitting in water. digging them up and digging down another foot or more and add some bark fines or potting mix. also mix in some dolomite lime in each hole. the ber is a result of the watering problem. how the calcium moves throughout the plant.

I expect, however, that this will be a little too traumatic for the plants and am wondering if I have any other options.

I agree with all that Terry said above so a couple of alternatives for consideration:

1. add additional 6 or 8" boards to the beds and fill with additional quality soil/compost mix burying the plants that much deeper in the process (you mention they are tall enough to accommodate this). New roots will form all along the buried stems of the plants. Cut back on watering.

2. assuming the current plants are indeterminate varieties, take cuttings off them to root for replacements BEFORE carefully digging them up to making the bed deeper. After digging deeper in the bed to improve drainage, remove the existing green fruit and replant the current plants as deeply as possible. If they make it - great. If not you have the rooted cuttings to replace them with.

3. accept that first year gardens are always plagued with problems and little success and that this set-up was very flawed from the beginning. But in the hopes of getting some crop, leave the bed as it is and cut WAY back on your watering regimen since you now understand the drainage problems. And at the same time use a piece of rerod or something else long and sharp to stab additional deep drainage holes down through the soil and the plastic. Then plan to do a major over-haul on the beds this fall (strip out the plastic and make them at least 2x as deep).

Just some ideas to consider.

Dave