Definitely ditch the hammer. That will not get this one done. Pretty sure of that. It will just bounce things around and out.

Looking at your photo (BTW, you live in a beautiful place - wow), you might have better access with just a single jack stand at the jack point behind the front wheel on the left side. That jack/lift thing is probably right in your way, and easy visibility / access helps. And you might also find that jacked like I'm saying, you won't be leaking any ATF at all out of there. I don't think I was.

Another finer point on a little thing - I did mine at night, partly due to time constraints, but I found (as I often do) that I have better visibility working on small dark things under the car at night time with a good head lamp, etc. vs. in the daytime when everything is bright and when I look under the car everything looks dark because my eyes are adjusted for the bright daylight.

Every little assistance might help get past this simple but tricky thing.

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2001 X5 3.0i, 203k miles, AT, owned since 2014