Your solution will help get rid of that condensation, but there is an additional solution to your problem.
I built our home in 1977 and had that same problem for a number of years...excessive dripping condensation on pipes and ductwork in the crawlspace under my home. Being on the waterfront of Albemarle Sound less than 50 miles from the Atlantic, we have very high ground and air moisture. Ground plastic does no good in such high air humidity.
Ventilation was the solution.
I ordered a 10" louvered exhaust fan (actually made for dairy barns) with a small 1/30 hp motor and installed it in a custom-made pressure-treated plywood and 2X4 door. I ordered the fan from www.wwgrainger.com
The crawlspace door that I made was 5/8" pt plywood with a 14" square hole cut in it. The hole has a single layer of pt 2X4s around it on the outside and a double layer of 2X4' around on the inside to A. accomodate the weight and louvers of the fan and B. hold layers of hardware cloth and screen on the outside.
I plug this fan in under the house and open all of the vents and let it run 24/7 year-round except for freezing weather.
That particular exhaust fan is about double the size of what the Tech Support man at W.W. Grainger recommended as the minimum size for the cubic footage of my crawlspace, as I believe that there is no such thing as "too much" ventilation.
Before you start shopping for an exhaust fan, calculate the cubic footage of your crawlspace (length X width X height (ground to subfloor).