"New" Thorens 124 sounds great, but...

Could the lift platform be at an angle such that it pushes the arm back to the rest when you lift it?

Why would you blow your money on needless mods.

So, I used a grooveless record to see what was going on. With no grooves, the cartridge flew to the middle - until I lifted it off the record, and it flew to the outside. And I can feel the attraction of the cartridge to the platter.

That combo seems like it won't work...

Take the top platter off and see what happens.

Thorens also made a non magnetic platter, known as the Zamac platter. It is a bit lighter than the steel platter, but has no magnetic attraction. It uses the same aluminum topper as the steel platter.

One thing that folks do is put a felt turntable mat between the steel platter and the aluminum topper, to get the cartridge further away from the platter. Of ourse, you will have to readjust VTA.

Another thing to look at is the anti-skate setting of your tonearm. Too much and it will drift back to the arm post. Good luck.

I have a TD124 modded by Greg Metz and I am getting the best vinyl playback of my life (after owning several other decks including a VPI Prime).
My first piece of advice is to call Greg.
Second-how familiar are you with TD124’s? Do you have the thin top platter that was original to the deck, or do you have the tall aluminum top platter that Greg offers as an upgrade? If your platter clutch still operates, you have the original thin one. If you have the tall top platter that Greg provides, there is zero chance of this being a magnetic problem. Since you say you can "feel the attraction to the platter", I am going to conclude that you must have the thin original top platter.
Btw, I too use a Benz cartridge, a low output Glider. I am pretty sure Greg has run out of the tall top platters and even if not, the tall top platter comes with the need for a new main bearing and typically a spacer to raise the tonearm column.
Are you sure your armboard is level to the platter? A poster above alluded to this potential explanation. If Greg provided and mounted the armboard, it would seem unlikely that this is the problem. 
Just for kicks, try disabling the anti-skate on your arm and report back if the behavior changes. Then try changing the platter mat. Then try changing the cartridge assuming you have something else sitting by.
Greg typically tests his work with a variety of cartridges, most old Shure MM’s. Right now-from what you have told us-I am guessing it is your platter and you will have to decide if you wish to switch cartridges or replace your platter with a non-ferrous one or opt for a tall aluminum top platter.
As to the poster above who commented about wasting money on mods, what a naive crock of crap! Just read Art Dudley’s articles which can be Googled. The TD124 was one of the best-designed and best-built turntables of all time. There is a magic to idler drives that the TD124 and Garrard 301/401 exemplify better than any others. Schopper of Germany and AudioSilente of Italy offer many upgraded components that help bring the TD124 to an all new level. Idler wheels, motor brushes and bushes, main bearing, motor mounts, platters. And then there is always the option of a high mass plinth though many-including Greg-argue that a lower mass plinth is best for the TD124 since the arm sits on the chassis and that a high-mass plinth is best for the Garrards since the tonearm sits independently of the chassis.

Early 124s had a ferrous platter. MCs became popular later, and that platter created havoc, just as you describe. So they made a new platter, non-magnetic. Swinging to the outside is repulsion, and playing with adjustments won't change the laws of magnetism. It may affect VTF too, so check it when the stylus is on the platter, then higher, and see if they differ: if so, compensate. But how does it sound when playing? If it plays and sounds as good as you hoped, then ignore the idiosyncrasies. It's a great TT. 

Classic "sticktion" problem.  You have a few choices:
1- change your cartridge to a MM or MI/Mc (Moving CROSS) type.

2- increase the distance between the cartridge engine and the magnetic under-platter.  This can be done by using a thicker mat or pad; I have seen leather mats that worked well.  I have tried a copper mat (Micro Seiki Cu180) myself and it worked well.

3- replace the magnetic sub-platter with a non-magnetic alternative.  I am not a fan of the TD-124 MkII style alloy platter.  Stainless steel is a great alternative.  Many manufacturers of these; some re-use the aluminum top platter and some don't.  Pay attention to the strobe disk on the bottom.  Some SS platter manufacturers use a stencil which is OK but they stretch easily and often are stretched or warped on mounting which is not a good thing.  The best bet IMO is the black-is-beautiful Schopper non-magnetic platter.  It's expensive but it's worth it.

Are you possibly using a lot of anti-skate ? Just lower the anti-skate or remove it if it is a string type. Then see if this anomaly continues. 

Thank you all for thinking with me. In terms of leveling and anti skate, I am confident that those are not the issues. When I replaced my Benz with a Hana SL, and none of those problems were present. In fact, it was utterly predictable. Likewise with a good quality MM. But when I put the Benz back on, the quirkiness returned. And so did the glorious sound.

BUT, I have compensated for the added downforce, and am careful when using the cue lever. And this is by far the best analog has ever sounded in my life. I am using the same tonearm/cartridge that I had on my last good turntable, so, I am comparing apples to apples. And to my ears, this is simply wonderful. So, I guess I will learn to live with the way that the Benz interacts with the platter (I do use a cabon fiber/cork platter mat to try to get some distance, and it doesn't do much - at least with the Benz). 

I'm actually very pleased, and I just hope this increased magnetism doesn't hurt the Benz Ruby Z long term.