I am having the most outrageous starting issues. Has 2.9 and v6. I've replaced every component of the starting system, solenoid, battery, cables to and from the starter and the starter itself. I've sanded and cleaned all the connections. Bought 3 lifetime replacement starters and inspected the flywheel. Even ran a starter cable to the mounting bolt of the starter to make the ground better. When it fails, you can hear the starter turn but the bendix does not engage. When it does this I'll leave it sit for a couple hours and it will start. The starters test ok at the shops after they fail so it's still going back to connections but idk. It'll start no problem the first 20 times after I replace the starter, than the bendix stops engaging.
If the starter is spinning you can forget about the cable connections and all the electrical parts. It's spinning; they have to be working. Almost surely there is a spot on the flex plate with the teeth worn away. The next time it acts up, grab the belt and turn the engine a little in the direction of normal rotation, then try it. If that works consistently, inspect the ring gear on the flex plate. If this seems to be affected by temperature and turning the engine doesn't help, you might check if the rebuilder has been using some kind of grease on the motor's shaft. Some greases get hard in cold weather and prevent that drive unit from sliding freely. You can dissolve it with WD-40 or Chrysler's MP-50. Those will stay fluid in cold temperatures.
If the teeth on the ring gear are okay, this typically happens with the starters with the tapered cover and only the single fat cable attached to the starter. It's not common, and it's really not likely on three starters, but if you remove that cover, you'll see a pretty significant contact that could be pitted. Push on the "pole piece" to open that contact so you can sneak some sand paper in there to clean them. There's two coils of wire that are half of the motor. One is bypassed with that contact so the other one makes a bigger magnetic field to pull on that pole shoe. When that contact opens, the starter motor gets stronger, and the magnetic force on pole shoe gets weaker. If that contact is pitted, the magnetic field might not be strong enough to pull that pole shoe down. This is the only starter ever made that can spin when the drive is not engaged.
If you have a starter with the solenoid mounted on top like all GM starters, the motor can't spin until the drive engages because it has to reach engagement before the contacts for the motor switch on. In that case you can only have a bad drive assembly or partially-missing teeth on the ring gear. Ford used three different starter systems around this time period. Only one used the starter with the tapered cover. The other two used starters with the solenoid on the starter. The large round or older square solenoids on the inner fender Ford was famous for are still used in those systems but only as a low-current relay, not as the high-current switch like it was since the '60s.