I use a toothpick to help get the tap root positioned. If germinating with paper towel I have found it is a lot easier to wait until the seed cap has kicked off. Then just plant 2/3 of the tap root in the soil with the cotyledons above ground.
I do the same. Sometimes, I'll take the tip of a knife and dig a little hole in the medium right next to where the seedling is lying, and then use the toothpick to gently nudge it into the hole, root tip down. Then lightly cover it. That way you're not really handling the root.
Remember, OP, it's a weed - it's hard to
stop them from growing. Help it out a wee bit with a toothpick if you like, but don't worry about making it perfect. Just make sure the entire root is covered with soil, and try not to bury it with the root tip pointing straight up close to the surface. The roots know how to figure it out from there. You may see some really weird, twisted roots at the base of the stem after the plant grows out a bit, but the plant knows what to do.