You could probably cover this stuff up in different ways also, or in addition to removing some of it. You could put bark mulch directly over it and cut holes wherever you wanted a plant (also drill holes for drainage here and there). You could probably put brick or patio pavers over it too. You would need to rent a fairly heavy hammer drill from your local equip. and tool rental and drill holes in it for drainage, probably one per foot or so, then you would put down an inch of sand and put your pavers on. Or, skip the holes and sand and just mortar stone or other directly to the asphalt and let the water just shed away. Another solution would be to have a small dumpster delivered to your house and then have a "bobcat" loader delivered for 1/2 day (fairly cheap!) and just rip it up, put in the dumpster, and be done with it. The company that rents the bobcat can deliver some loam and mulch to you too. Keep the bobcat all day and get all your rough landscaping done for probably under $1000!!! Its fun too! When spreading loam or mulch with a bobcat, have the pile off to one side, take whole scoops away to the farthest area and work back from there. They don't work very well for trying to spread stuff out directly from a pile. I'm not a landscape professional but I have done some of this stuff at my house and saved tons of money.