Were it my pour, I'd use a day laborer to dig out the area for me, frame it with 2x12s, and wire in some reinforcement mesh. I'd have the laborer try to keep the bottom flat, but if he overdug an area, I wouldn't have it filled in with loose dirt. I'd leave it to be filled with crete. Concrete likes a very firm base, which keeps it from settling.
Then I'd hire a concrete finisher the day I had the concrete truck do the pour. He'd make sure it was flattened and smoothed, then once it set up a bit, he'd very lightly broom it for better traction.
After it's cured for a week, I'd come back and fit the asphalt to the concrete for a smooth transition.
The good thing about concrete is that only the first yard costs a lot. The rest comes along for the ride. Around here, it's $140 for the first yard but only $500 or so for a ten yard load of it.
If you use your own dump truck and laborer, it shouldn't cost you over $1,000 all together. Just do it!
-- Happiness lies in the joy of achievement and the thrill of creative effort. -- Franklin D. Roosevelt