Curtain drain in the crawl space - Part 2
OK Peter, next steps are easy compared to what you have done already. The first step is going to be install your foundation grade water proof insulation to the walls, from footer to the top. This comes typically in a sort of tongue and groove panel. Clean the excess dirt etc. off the walls and apply the mastic, then just stick the panels to the wall.  Depending on what brand you buy, check with the supplier's recommendations for proper installation techniques.  They are all pretty similar however. Since you are installing it in a crawl space on the inside of the wall instead of the outside, getting a complete water proofing layer of the mastic is not that important.
I would highly discourage you from using the old spoils as backfill. You mentioned it was a clay base which is very poor for fast drainage. Please use the stone and gravel as I described in your last question. This method will assure you very good drainage. If you buy the drain tile (flex pipe) that is prewrapped, that will save some time and frustration. So, second step is to install your tile, and couple it through the foundation to your existing system.  Complete your backfill, level out the area best you can then start your plastic vapor barrier. I would use a 6 mil minimum.  Be sure to carefully tape all seams and neatly fit the plastic to the walls and tape it.  The idea is to create a good vapor proof cell, keeping moisture out of the crawl space.  You may consider some ventilation for summer season and closing said ventilation during the colder, dryer months.  Sounds like you are well on your way. Don't short cut now, you got a lot invested.  Good luck.