I like the contractor's thoughts but would upgrade the pipes under the wall to pipe material that can withstand some weight and movement. Nobody can forecast what the settlement and movement is going to be when clay is involved, but the pipe needs to take all the weight if necessary. 4" iron is a common for municipal water & sewer pipe - which keeps the price reasonable. Get ductile iron if you can and cast iron second choice. For as little amount as you are looking for I would see who local stocks overage from projects. Ask at the water utility. There are also decent heavy wall PVC for that matter - but not at Lowes/HD.
About the sock, we had a flood here & rebuit some perf drainage with some left bare, some socked, and some with double sock and PVC peanuts. Some silted up and some hasn't yet. My latest effort is to lne the bottom of the ditch with strips of geotextile 3 or 4 foot wide, put down an inch of washed gravel, then the perf pipe, then cover the pipe completely with gravel and fold the sides of the geotextile fabric over it all and backfil.
That system worked until the willow roots from the windbreak found their way into the end of it.... Now I have to roto-root my drain pipe every year.
So my last piece of advice is whatever you do, make it "roto-rootable". If 300 ft long consider putting in a pair of back to back risers for access to the pipe every 100 feet
luck,
rScotty