If they both rock, I would check the rail for flatness.  Make sure it's not twisted.  That could be your problem.

Peter, no offense taken!

  I believe this may have been some user error....

I'm really used to doing things a certain way and didn't really bother trying to find out if I needed to do things differently with a new tool. Its weird that I've never had any kickback from my boss's makita.

Would the saw be less inclined to kick back with a courser blade (such as a 28 tooth "universal")?

I'm still less than happy with the wobbly bases. I checked the Makita with a straight edge and it's got a big high spot on the bottom of the base. So it's getting chucked back to the retailer. Most of my tools are older Makitas. I've been really disappointed with the QC on the last few new Makita tools I've bought.

Oddly, the Festool replacement base only wobbles on the lower half of my rail. Hard to say what the issue is, base or rail. The rail has so many different planes on it that it seems impossible to check it across its width or for twist. I would think that the saw would press the rail more or less flat as it traveled along it.

If you think about where you're pivoting the saw in a plunge, the direction of the blade travel and where the meat of the cutting is happening you'll realize why the track saws are different when you plunge. 

With a traditional sidewinder you pivot in the front of the base plate.  As you feed the saw down, you are doing most of your cutting on the back side of the blade which is spinning down into the material.  You hand is directly above applying downward pressure to complete the plunge.  It's a reasonably controlled cut. 

With a tracksaw, the pivot is in the back of the base plate.  You lean the saw head forward, you are doing most of your cutting on the front side of the blade which is spinning up from below.  As the blade grabs it wants to pull the head down (while you are also applying downward pressure).  The only thing counteracting this is the force of the spring on the saw head, which is negligible.  Similar to a climb cut, you lose control.  So the saw head gets sucked down instantly and pushed back as the head travel bottoms out.  While it's a good substitute for your morning coffee, I don't recommend it.

As to your baseplate issue, I'm not familiar with the Makita, but I would hazard a guess that the kickbacks may have tweaked the base plate?  Try a new one and check it for flat on a truly flat surface before using it.  Then put on the rail and check that.  Don't plunge unless you have the plastic stop block Peter talked about.  Drop the saw head fully while on the track, then feed the blade into the wood.

I doubt the rail is your issue, unless it's visibly bent, which you would see sighting down the rail.  Even if it had a little twist (so little you could not see it by eye), it should lie flat on a piece of plywood. 

Checking your bevel mechanism as suggested above is a good one.  It's possible something has bound up and created some tension (or a good knock during shipping).  Loosen up the bevel knobs, move the saw out to 45 and back just to check for anything obviously causing tension, lock it back at 90 and check the base plate again.

Correct, if you use that stop block Peter recommended with the tracksaw, it will allow for a controlled plunge.