The slippery feeling of the water meant that the softener was working; there was less than 1 gpg of hardness in the water. Finding a softener there means the water is hard. Feeding a softener salt is much less expensive than living with hard water and all the hidden expenses of hard water like increased water heating bills, failure of water heaters, premature wear of all things washed in hard water and the increased detergent and cleaners that must be used and the wear on water using appliances and fixtures.
Reinstalling the softener would be a good idea. Sanitize it with a 1/4 cup of bleach in the 5 gallons of water in the brine tank and doing a manual regeneration. Add part of that 5 gasls of water to the water in the brine tank if there is any.
Depending on where you are, your drop pipe down the well may be galvanized. That length of PE pipe and the water and pump won't weigh 300 lbs.; less than 120 lbs. is my guess. The galvanized will be much heavier and may be in 21' sections that you must unscrew to get apart.
A C clamp won't work on PE, it would collapse the PE and probably damage it and it would slide.
Your backhoe is fine as long as you lift straight up. There is a large vice grip type clamp made for holding PE pipe. They are sold by pump and some plumbing supply houses for maybe $75. There is a Pipe Vice too, it sits on the casing and when the pipe starts going back down the well it grips it due to a tapered shape.
You're right about the leak flushing dirt into the water. And a disposable cartridge filter is not a good choice to filter a lot of visible dirt/sediment.
Build a shed/pump house and get a pressure tank for in it. A prebuilt shed from Lowe's etc. would work, just make it so a drilling rig or pump derrick truck has access to the well all around.
Gary
Quality Water Associates