Learn English – How to position the tip of the tongue when pronouncing /s/ & /z/

A few points come to mind (as a linguist, but native speaker of a nonrhotic dialect):

1. Pronounce ɹ correctly, in the way that you’ve recently discovered: symmetric on left and right sides; no sideways twisting—rotation isn’t rhotation ;-)
2. When I pronounce ð and θ, they are not always apicodental (tip of the tongue against the teeth), but often approach laminodentals (blade of tongue against teeth). However, after n and ɹ, I have to make them strict apicodentals. So, check you're doing that.
3. Practise saying bother no one. To produce ɹn, your tongue makes a similar transition as in ɹð, ɹθ, but it’s shorter. So, it might be easier to wrap your tongue around (pardon the pun). Likwise: bother Danes/Thais.
4. Then practise they’re there. Same transition as the one you’re interested in, but the longer vowel may ease the transition. You may also find that you can make the apicodentals barely more than a tap.

After that, hopefully bother them will be less bothersome.

I watched the first Youtube video you referenced, done by Rachel, and I think several of the observations are good, but overall, it misses the point. The important difference between dark l and neutral l in English is retraction of the tongue body for the dark l. (I'm calling the non-dark l "neutral", because I don't think l in English is truly light -- just sometimes not dark.)

The position of the tongue tip doesn't matter. When the body of the tongue is pulled back, that may affect the position of the tongue tip, but that's just because the tongue tip and the tongue body are connected -- they're both part of the tongue. It's the retraction of the tongue body that makes the l dark, whether or not there is any difference in the position of the tip.

Rachel talks about the pronunciation of "real" and observes, correctly, that there is an extra vowel sound that intrudes between the [i] and the [l]. But that is not what makes the [l] dark. When the tongue body is pulled back for the dark l, the body of the tongue has to move from front to back, since it was pushed to the front to make the [i] vowel, and it has to be pulled back for the dark l. To get from one place to the other, the tongue body has to move through an intermediate central position, and this is what Rachel hears as an extra vowel sound between the [i] and [l]. This central glide is predictable if you have a correct idea about how dark l is articulated.