Do your grading first; you want a solid base so the asphalt thickness can be consistent.  Grade and roll everything before you spread asphalt.  A vibratory roller is almost a requirement for a good tight finish.  If possible, keep your lifts to less than four inches (loose) at a time.  My observation has been that a sheepsfoot works best if you can find one.  Some really nice field roads and yards at a customer of mine were made by grading, rolling, laying out a layer of geotextile, then rolling the asphalt over the cloth.  It's holding up very well to heavy truck traffic.  It takes a lot more work, but carrying it to the site rather than pushing it seems to result in a nicer finish.  I think if you blade it you tend to segregate coarse from fine more than if you bucket it into place.

Grading works - just don't over do it. Grade a crown into it, so water drains to the sides. Asphalt does wash - just not as bad in lighter rains. But, in heavy down pours, if it runs down hill, it'll wash - that's why you need a crown to get it the rain off to the sides quicker.

Water works for packing - Diesel will dissolve the oil in the asphalt. Too much and you're in trouble, but a little would work. How much is a little? Maybe 0.015 gal per square yard (WAG on my part based on how much CSR2p [base oil] is applied on a chip seal over gravel road, which is about .3ths g/sqyd).

When you finish, you could chip seal over the top of it and have a asphalt road at that point, it wouldn't wash then.  

Don't know how steep you are talking, but have packed asphalt millings (3/4 minus millings), with a about a 10 degree or 6 to 1 slope and the small steel drum vibrator packer worked . . . . . . A 13 or 15 wheel rubber tire roller would work also, pulled by a tractor ?

If you are working with millings bigger then 1 1/2 inch - then you better plan on a sheep's foot packer . . . . . Dozer tracking over should help break and pack also. We used a skidsteer and bucket to place and level, then 1500 lb smooth steel drum vibrator roller, it could have been larger and heavier, but it worked.

Keep watering them as you place and pack - and water the heck out of them for final rolling/packing and keep going over them packing. They will get hard.

Yes, simple water garden hose or if you are doing farm roads/drives in different areas, then a water tank with home made spray bar. Soak it down and roll it out. Water as you are spreading and it really packs in hard. I'm not a fan of diesel - diesel is or was used as a cleaning or clean up agent on asphalt equipment. So you are dissolving the oil in the millings . . ..  . . .

There are many different types of millings - seems most of the milling projects around here are pushed pretty fast and the roads are broken up pretty bad, so the millings really come out as Chunks of asphalt. Millings here are never given away - they are always recycled and worth more per ton (if you could talk a pit out of some) then crushed granite . . . . ..   The reason the millings come out in chunks here is they handle better for final crushing later. The bigger the chunks, the less it sticks together or make a solid pile like some describe in their reply's.

Frankly, I'm surprised any State DOT, County Hwy Dept, City or Township would allow millings to simply be discarded . . ..  they have greater value being recycled into a new hot mix or as base material for the road . . . . . . . . .

interested in learning more about this  'geo-cloth'.   

Just be careful that you are getting the top millings, not from a repair job where they are cutting down to dirt to fix soft spots in the road.  I got the latter and might have well bought dirt, cause that is what is mostly was.  Never did set up and is still soft even after repeated attempts to pack it.