You got a lot of good suggestions, but understanding a bit more, I might another comment or two. Yes, don't use a wobble dado, use a decent stacking one, and if you have the stops figured out, and use that same backer board, sounds good. As to pushing the saw back in, definitely it is a bit safer, as it won't grab. However with a big stacking dado, it does still have 2 drawbacks.
1. if you push it quickly it will tend to "raise" the post slightly. Probably not a big deal, as it is a post after all.
2. perhaps more importantly, as I understand it, you are mass producing these and want the fastest way to do it. When speed is involved, I would get a bit concerned about pulling the saw out, sliding the post behind the saw, then pushing it back in. You have a big saw spinning at the end of the travel, too close to you while you are manipulating a big piece of wood. You might get too close to it, and the piece of wood also is able to slide and hit that saw too. yes, you could make a "track" that would keep the post in its groove, but be careful. Radial arm saws are not known for their safety. My late father in law (a contractor) wore a glove on his left hand, to cover up where he had sliced off 3 of his fingers, on a radial arm saw.
So while I agree that pushing rather than pulling is less likely to bind, I worry about the act of moving the wood in and out behind a saw blade, same in moving the stops. If you do this, remember to move the stops while the blade is behind the wood. Good luck