Unable to remove push-pull stopper from tub drain

Question

I need to remove our push pull style drain stopper in our bathtub so I can get the snake the drain. I've looked at several videos of all seemingly different style lift and turn stoppers, and none have helped.

Here are the best pictures I managed to get: https://i.sstatic.net/xOTtr.jpg

Some info about the stopper:

1. There is no screw under the cap/knob.

2. There is a ball bearing on the post/rod that depresses when pushed shut (spring-loaded?).

3. The cylinder holding the rod has a flat side, but is inside the drain itself. The ball bearing doesn't act differently when turned to this part of the cylinder.

4. The cap looks like it's screwed onto the rod, but the opening is barely large enough to get needle nose pliers in. I have some small vice grips, but the nose is too get a good grip on the center rod.

5. The cap + stem rotates when turned, whether popped up or down

6. I think the drain/tub assembly are from Danze, but a lot of the other drains in this house are Kholer, but I couldn't find any useful information regarding this style stopper from them.

Any suggestions? Short of dissembling the pipes or ripping it out with a crowbar, I'm kind of out of ideas.

For what it's worth, the stopper in this question is likely the same, but the accepted solution was to use a plastic drain stick, which I've already tried: How do I remove a push-pull tub drain stopper? . Also, it doesn't actually answer the question: how do you remove this stopper?

Top of the stopper

Inside of the stopper (note: ball bearing, no set screw)

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EDIT: I never managed to get the stopper out. I think to remove it, I would have to take @Programmer66's suggestion to go in from the access panel in the hallway and open up the drain pipe to remove it from there.

Since my plastic drain stick was coming up clean, but was long enough to reach the end of the drain itself, I figured the clog was further down than that. I removed the cap on the overflow drain and used a 15-foot drain snake to remove a hair clog deeper in the pipes.

Answer 1

You just have to grip the whole top assembly with a channel lock or vise grip, taking precaution to not damage the finish. Slowly turn counter-clockwise. Also trying squirting WD-40 with the tube under the cap, Wait a few minutes, and try again. Removing the cap off the stem will reveal the pop-up mechanism. I have a picture of my cap removed. Either the cap will come off at the top or the whole stem will unscrew at the "Cross" about 1.5" down in the drain. The stem in the middle of the drain will unscrew from the cross bar you see even if the cap is stuck. Using WD-40 will either loosen the bottom or top or both. When using the Pliers, use a rag to protect the edge and give gentle twist counter-clockwise.

Also try this using a small wrench, The size that slip on the flat sides on mine was 10MM, about 3/8". In the tub, it should be flat enough to just slip the wrench in.

IF the whole assembly is rotating, see picture below, then the retaining nut beneath the tub has loosened. Remove the retaining nut, disconnect drain from downspout, and remove the complete assembly.