After removing the cones and axles, I tried something new. I once read about Belgian bike mechanics putting grease ports in hubs to force grease into the bearings from the inside out. So, with that in mind, I drilled a hole that I could later tap, or jam a syringe into in the middle of the hub with a flexible shaft die grinder:
I then taped the hole over, blew out the drill debris, cleaned out the cups with a cotton swab and applied a liberal amount of grease to the bearing surfaces. I used lithium axle grease. If it's good enough for car axles, it's good enough for your bike.
All that grease makes a nice sticky place to put those bearings with a tweezer and make them stay. After putting in all the bearings, I tightened everything up. It took me multiple iterations to get the cups and cones not too loose and not too tight. It always does. I guess if you're a full time mechanic, you get a feeling for this. At some point, maybe after 1k miles or so, I'll try injecting grease into the port until it squirts out the sides, wiping off the excess. I'll let you know how it goes. Until then, they spin like a new set of wheels and should carry me to work and play many more times.