Hi Myka
Nice, I really like your enthusiasm. Don't disturb the roots this year, or for 2019. After this severe a pruning the tree will need the roots undisturbed so they can heal the tree and regain vigor. The tree needs to grow before attempting to repot. In 2020 when you repot you may indeed remove a ''carrot like'' coiled up tap root. IF you don't do a bunch of pruning of the foliage in 2020.
Your wiring job is not bad for a first effort. Practice will make perfect. Colin Lewis has a wiring tutorial on ETSY. You have to register, but it is free.
But for a ''first effort" it is really pretty good. So even if I, or others are critical, you have done better than many I have seen, so keep up your enthusiasm. You can only learn by doing.
You might try repotting one or two of your trees before styling. Repot into a low and wide growing container, box, Anderson flat, large bulb pan. One that holds the same or more potting media than the nursery pot it is currently in. Less than 5 inches deep, 4 inches is perfect. Do the major root work needed to get it ready for a future bonsai pot. You can remove up to about 50% of the root system, maybe more. Use a good bonsai soil, one that is mostly pumice. Let the tree get established and growing without any significant pruning. (less than 10% of foliage). Let it alone for 2019 after repotting, then in 2020 do the styling, if it buds out well and grows in the beginning of 2020.