Try to get the whole core and z axis in the video. It will give us a better idea of what the issue may be. My working area is 600x900 and there is nowhere near that much flex from the rails. The only time i see flex like that is when the bearings in the core have loosened up. Normally flex like that is the z axis bearings after several long jobs. Contrary to popular belief, nylock nuts can and do loosen up. I’d try to figure out the issue you are having instead of tearing it apart not knowing what the actual problem is.
Just my 2 cents…
This isn’t my usual way of diagnosing a problem. But I have no experience at all with the mpcnc or any cnc for that matter. I know I had over tightened some things trying to get the play out, that is why I replaced some parts. And making sure the large size isn’t the main problem crosses that of the list too. The small build did the same. But gave very little room to measure and feel/move things.
It is back to the original size and build according to the manual.
That should be a good base to work from trying to find the problem.
We are here to help if you need it.
Thanks. I’m sure I will need plenty of help. 
I was looking for a way to show the flex I see. But somehow I can’t see it in a video or it looks much worse than it really is.
I needed a bit more control. This is what I came up with.
I put a weight (2.5 kg) on a piece of rope and hang it from the end of the end mill over the edge of the table.
I put the dial indicator on 0 without load and it moves 0.23 mm with the 2.5 kg load.
In the build instructions for the Burly MPCNC I remember reading something about belt tension and cutting forces. That was about cutting alu and according to Ryan it takes about 2.4lbs of force to cut aluminum
Now I found some info about side load in an old thread here. Maximum side load
In that thread Ryan says most MPCNC’s (Burly or Primo?) can do 1.9 kg.
That gave me another idea. I put the same weight and rope on a piece of MDF and see what happens when I let that weight pull the MDF against the end mill. Very little cutting and a burning smell. I have to push hard to get it cutting. That was with 6 mm DOC. With 2 mm it will cut and with just 1 mm DOC it cuts cleanly and quick.
To me that sounds like the cutting forces are way to high. And the only thing I can think of is that I have crappy and mills.
I’ve got a video and several posts about that … 
The solution lots and lots of posts later:
Thanks.
This post shows pretty much what I’m seeing. Der Froschkönig - Lowrider 3 in Oldenburg, Germany - #170 by Tokoloshe
It looks like the forces build up during milling and get released when the mill gets to the end of the grove.
Also the video you posted shows what I see over here.
I did a new test with lower RPM and I think I over did it a little. I have to guess, but I thing it was around 7000 rpm. And that was to low and increased the forces even more, resulting in missed steps. First in X and later on in Y too. All with a 1/8 bit and 6 mm DOC. Clearly the forces got to high even with a small endmill like that.
Before I go try different thing I’m going to get some new and hopefully better endmills.
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I calculated cutting forces on my LR3 with the parameters I use, and reach 7,27Kg when cutting Plywood with 6mm single flute endmill, 6mm DOC.
I didn’t try these values on the Primo, but I thing it can reach similar values, maybe lil lower.
At this value the LR is at it’s limit i think, because when the endmill get worn starts to appear some oscillations, but it doesen’t skip steps yet
The lower RPM increases the forces only due to the increasing of the chipload.
Reducing the rpms decrease the cutting TORQUE, but this is related to the power of the spindle, not on the steppers.
Got the new bits today and did a quick test. It was a bit noisy and didn’t sound great.
But the 50x50 square was accurate, even with an 8 mm DOC.
The finishing pass now sounded like it was hardly doing anything (like it should I guess if the rough cut is close to the needed size)
No funny movement visible anymore.
The new bit is a single flute 1/8" bit. When cutting full width over 3 mm DOC is sounds like it is struggling.
Like it is vibrating/bouncing. When widening the slot with around 50% step over it does fine. Even with an 8 mm DOC.
I have to start playing a bit more with feeds and speeds. But the few test I did didn’t help much so far.
To me it feels like it need higher RPM’s, but the spindle is already maxed out at 12000 rpm. Lower RPM’s sound worse.
At least it is working better now and I know I have part of the problem fixed.
Thanks Philipp. I couldn’t any bits locally for a reasonable price. I found the bits you ordered in the link you posted. Even with the little higher shipping to The Netherlands it was still a lot cheaper than what I had found. And with the bits from Sorotec I knew someone had success with them.
Yes, that is right. But I think with the bit already not cutting great, the lower RPM’s made it even worse.