youch pvc with fittings to boot. cheaper pipe = black poly pipe (err i guess i should say more of a hose). (i don't remember the exact name) menards, lowes, homedepot sell it, normally gotta ask for it. to find it. comes in large rolls 4 to 6 feet in diameter. buy it by, 50, 100, 200, 250, 300, 500, 1000 foot lengths. use barb fittings. if you snake it into the trench so it weaves back and forth side to side in trench, helps to ensure any settling issues. and ground movement, will not cause issues with the pipe.
the 1" sched 40 pvc hard pipe and fittings can take a beaten in trenches.
next time once trench is dug, and you put pipe in. fill pipe with water. before covering it up with dirt. to help hold the pipe down. and make sure you get it back filled and properly compacted. before rain hits.
you have a box blade, tilt that 3pt hitch all to one side, using both side link adjustments (normally just one side link adjusts), if you can adjust both sides even better). and toss one corner down into trench.
3pt potato plow can dig down and make a trench for you. pipe layer (not sure correct name) looks like a potato plow. just has a large "blade" that sticks down into ground. and you just drive along with tractor. and it opens up the trench. some of them you can use roll of coil pipe, and inserts pipe as you open up trench. never even having to deal with pipe, exception beginning and ends of trench.
everythingattachments, grainger, tractorsupply. one them should have one of the 3pt devices.
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for pipe in trench. time to chop it up and get it out. not sure if a bolt on tree spade for FEL would work, in trying to pop out the pipe from dirt, without causing damage. mini ex (mini excavator) more likely be the ticket, beyond manual labor. due to overall control of the bucket.
look in old paper phone book (not internet) and look up "machinery rental" there be trenchers, to mini ex, to ditch witches that can be rented.
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10 inches seem rather shallow. granted were i live frost line is 3 to 3.5 feet deep. and i need to get any plumbing in, below frost depth. you might want to ask around. to see what code / regulation state for depth to put pipe.