I'd use wire instead of fiber mix. Or maybe wire and fiber. I have poured lots of concrete. Have two power towells now plus all the drags and bull floats. Pour it manual. That machine is a disaster waiting to happen.
Yes, fiber and wire do different things.
Concrete is very strong in compression, but relatively weak in tension.
Properly rebar reinforced concrete is twice as strong as unreinforced concrete. The compression happens when a heavy truck passes over a well compacted, deep base. The latter happens when there is a lack of support underneath, and the concrete flexes downward, like a beam in a building.
Glass or plastic fiber helps with surface cracking and spalling, especially during drying. It doesn't add much strength to the final concrete. There are spiral steel "fibers" that are sometimes used as a strength additive, but even more than glass or plastic, the steel fibers tend to clump during mixing, which does away with their strength. It is very technique driven, and dependent upon not having water on the surface, I.e. ok for a warehouse floor, but not for a driveway, especially one that gets salt.
Rebar, 3/4 of the way down on lots of supports (chairs, preferably plastic or concrete), wired together so that it does not get stepped on and pressed to the bottom, acts in tension to support the concrete and helps reduce cracking caused by heavy loads or a poor base, or, say ground squirrels.
Lots of information here;
Concrete Rebar: Everything You Need To Know [plus 8 Main Types]
(You can click here to download a printable version of this article.) Steel fibers and rebar have some things in common. Both are made of steel. Both are used to reinforce concrete, and both can be found in floor slabs. Because of those common features, it is tempting to think of the two...
www.concretefibersolutions.com
@Creamer In answer to the original question, this doesn't sound like a DIY job to me, and as others have mentioned, I think that the pricing is off.
For DIY, in addition to pouring, concrete requires good surface work (floating) to milk more cement to the surface to make a harder, more water impervious layer at the top. You need to be doing that at the right time after pouring when the concrete has just set enough. Concrete waits for nobody.
As
@Have tractor will travel mentions, you could break it up into small 12x12' chunks, but why demo out a reasonable asphalt base? I would level up the base, tar it, add fabric (geotextile), tar it again, and pave with 2+" of new asphalt. If you are worried about loads, talk to your asphalt supplier and get base asphalt put down which has a coarser mix of gravel, but is stronger. Repave with a second layer of finish asphalt in a year or two, if you want a super smooth driveway.
All the best,
Peter