Your land and surrounds are interesting. The oaks appear to be about the same age which indicates that it may have been farmland until about 30 years ago. The land is disturbed and eroding. Your first expenditure should be hiring a landscape firm to hydroseed (without adding grass seed to the mix) all the loose soil. Then stay off the area for a year giving it time to stabilize. Frankly, I would not plant the slope. Let it revert to nature, weeds, brambles and the natural vegetation. Then concentrate on planting shrubs around the upper edge fading off into the trees. Do a search for "shrubs for shade + Missouri" where you will find numerous varieties suitable for your situation scattering them out and about. If you wish to spend the money construct a retaining wall in the sunny section along the drive, backfill and develop a perennial/shrub garden. Much easier to care for. This will take the emphasis off the hole in the ground.

It is impossible to keep critters from passing through a planted bed, but so long as you don't cultivate plants that pile up thickly with plant debris, they would not be inclined to make it a home. I hope it is just camera tricks, but the walk at the back of house appears to be sloping toward the house. If true, that would be worth fixing, as surely, a large amount of water will come off the hill at some point. At the end of the flumes, it appear that gravel is piled above the flume outfall height. This is going to create somewhat of a dam. It will drain out at the end of a storm but will hold some height of water during a storm when there is heavy flow. I would plan to be out there with an umbrella observing exactly what's happening in order to know if something needs attention. Do you need to be careful of wildfires? If so, see if the local municipality has a list of recommended groundcovers. Do you need shade at that side of the house? Some tree forms along the hillside would help hold the soil in place while not blocking the view. The steps to the top (nice wide ones) sound like a great addition if there can be a special viewing spot created there. What flanks your property on the other side of the hill? As one example, a tall bamboo forest (such as Oldhamii) with groundcover below, would look great. It looks like you have enough room at the end of the house for a more or less linear patio. One with some boulders could look nice.

Wow. I struggle to capture steepness in photographing my slopes, but yours looks nearly vertical. Either you're a great photographer or you do have a real challenge there. If the sage has roots that hold the soil, why not increase it asap? Start cuttings and see if what you have can be divided. Add a grass that can also be easily propagated. I think the book Gardening in a Post Wild World would be helpful to you.

"Placing a couple layers of cardboard under the mulch will also help." I wish that were true!! It is almost impossible to smother ivy roots. They will just wait until the cardboard breaks down and then grow right up through any mulch. I have seem them grow through landscape weed fabric from beneath the fabric....it is almost NO deterrent. In one situation I consulted on, they had covered the area with a heavy duty plastic tarp. The ivy roots just grew laterally under the tarp until they emerged from under its edges, greatly expanding the territory it claimed.