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Those 'awful' roots are a sign of good health. I will assume your first orchid is a Phalaenopsis NOID. Many orchids grow on trees instead of in the ground, and their squiggly roots help anchor them to the trees. Keep the roots; mist them every once in a while. They turn green when wet, and it is pretty cool.
The reason they turn green is because they contain the green pigment, chlorophyll, that is used in plants for photosynthesis. Since the roots are usually exposed to light in nature, they are used by the plant as extra sugar-producing appendages. The outside layer of cells die, forming a white or gray 'skin' over the green part, and this layer helps mop up water droplets from the air and keeps them until the live root can absorb them. Roots in a pot or a flask usually contain less of these dead cells, called velamen, because they are already moist enough and don't need to photosynthesize.
This is a long way of saying DO NOT CUT THE ROOTS!
To reflower the plant, you will want to make sure night temperatures are at least 10 F lower than day temps.

 

If you want to add more medium, repot it completely. You will want to pot it in sphagnum moss. Orchids need air around their roots, and adding fresh medium on top of older medium is a very bad idea. The older medium will decay quickly once it is covered up, and will become mushy and anaerobic. Needless to say, this is bad for the plant; not only will the roots in the pot die, but disease can take hold in the pots. I'd just leave it for 6 months or so, unless the medium starts molding up. BTW, few orchids grow in soil. Most need to grow airy mediums such as bark, moss, coconut fiber, bricks, house insulation, shredded tires, etc.. Even terrestrial orchids like Paphiopedilums grow in humus or moss, not garden soil.

 

Could you send a pic of the soil itself?

 

No, that's soil for terrestrial plants. Orchids are epiphytes in nature which means they grow up in trees with they're not parasitic. The rainforests get crowded so there's not much light on the forest floor so they grow up in the trees to get the advantage of extra light etc. Because of this they need very airy media, not soil. Go for a specific orchid bark mix. Terrestrial plant soil will smother the roots and kill the plant quicky.

Edit: also sphagnum moss and sphagnum peat are different things. Peat is the degraded form you want the actual moss.

 

If it really is peat moss, it isn't suitable. Peat moss is partially decomposed sphagnum, and it doesn't hold enough air for orchids to grow in it. Use live sphagnum or New Zealand sphagnum moss. It comes in bricks or slabs that you soak in water. It should be light tan when dry.