Let me get this straight in my head....You removed and de-nailed hundreds of BF of white oak flooring, ran it over a 60 year old powered hand plane and want to reinstall the flooring?
Were the nails you removed cut nails? Square tapered shanks? When I was kid, old timers used cut nails and hand drove them into the flooring.
You should look up one of the installation guides for oak flooring. NOFMA (National Oak Flooring Manufacturers Association) would be a good start. I used to do Expert Witness testimony on hardwood flooring and the guidelines are a tedious but worthwhile read.
From what you said and as I recall.....
The gapping in the original job was probably caused by bringing the flooring into the house and installing it before it had a chance to acclimate to the local conditions. Colorado would be very dry and new flooring may have been too wet for the local conditions. If you have kept the flooring in the same moisture content as when you removed it, it has had plenty of time to acclimate by now, assuming you did not move it into a moist environment to work on it.
What is the subfloor? It affects the nailing. If it is sixty years old, I assume it is either diagonal sheeting or actual plywood and not OSB or Wafer Board, but from your response, I don't know and don't know how old the house is.
As far as nialing goes, learn about Nail Pops. Nails tend to get pushed back out by seasonal swings in moisture content in lumber. The roofing industry "solved" the problem by insisting the nails be long enough to drive all the way through roof sheeting. The drywall industry solved or reduced the problem by using shorter nails with ring shanks and ultimately screws.
IIRC the flooring industry wants you to nail through the sheeting but, NOT into the joists. Nailing into the joists gives the joists "purchase" on the tip of the nail and may allow it to push the nail back out. I know this is hard to accept, but the drywall industry tried longer nails and it was a disaster, the studs and joists squirted them back out and it actually increased the number of nail pops.
I would use an air actuated flooring nailer. The nails are thin and wide, and sawtoothed on the edges only. I would stay back about 3 to 4" from the ends and nail about every 8" along the edge.
The floors I have laid over plywood, I did not use 15 lb. felt or any other underlayment. At the time I was convinced any cushion under the floor would lead to squeaks. I have laid about half a dozen floors that way and they don't squeak.
Also, be sure your subfloor is clean and as flat as you can get it. Also check it for loose nails and screw it down tightly to the joists.