Definitely remove the exposed roots, and, if it's practical to do so, leave the fresh cuts exposed for a little while. If you cover them with dirt, there is a little bit more chance of pathogens entering through those cuts.

This is a spectacular time to prune the roots that need to be pruned. Doing it now will minimize the time it takes the tree to seal back over the cuts.

I can't tell much from the picture, especially since it is appearing upside down. I tried looking at it by turning my head as much as I could without suspending myself from the ceiling, but that didn't really help. From your written descriptions though, it sounds like you are right on track.

I agree with brandon. Do what you need to do, and don't look back. It is better to make these changes now than later. Just keep a watch on them over the summer. You may need to increase water at some point.

Arktrees

Green side up!

You won't hurt that red maple at all. This species grows annual feeder roots like this into mulch layers as a matter of course.

Prune off, mulch, and go on. Your trees thank you.

To make the photo appear right side up, just double click on it.

Those are adventitious roots that can be safely cut away at any time. You need to expose the flare and the first structural roots. Those adventitious roots only grew because the tree ended up with too much soil piled up around the trunk, unfortunately a common phenomenon with woody plants coming from many of even the most highly regarded growers. It is not uncommon for me to have to excavate 2-3" away from a tree when I plant it. A hori hori knife is a girl's best friend.

Double clicking is so much easier than suspending oneself upside down for the ceiling!