The people here who are happy with sand over the long term are almost always located in a dry climate and have the sort of personality that actively likes the daily scooping.

New England not being dry, you'd need to have your run fully-covered to have a shot at it working for you.
The first thing you need to do is to fix your drainage. No bedding or management system can compensate for bad drainage.
Where is the water coming from?
If it's running off the roofs of nearby buildings then you need to install gutters to direct it away.
If it's running across the surface of the ground and passing through the run you need to install French drain, dig diversion ditches, and/or create grass swales to direct the water around the coop and run.
If it's puddling in a natural low spot in the ground you need to either move the coop or bring in fill and have the land re-graded so that the coop and run sit on an elevated area instead of a low area.
Coarse wood chips -- the sort you get from a tree-trimming service -- are usually considered the gold standard for managing mud and/or odor. They're absorbent but have good airflow and, unlike many other options, resist packing, matting, and the development of anaerobic pockets.
Combined with things like fall leaves, dry grass clippings, and other yard waste they make an excellent base for a deep litter system, where the poop and bedding compost together.