How to pronounce smooth and smoothie

I have previously written about the different pronunciations of the th (an example of a digraph) in English, see this post. Today, I want to discuss the tricky words smooth and smoothie, which are very often pronounced incorrectly. The main reason is that many nonnative speakers feel uncomfortable with the sounds [ð] and [θ]. However, that is not the whole story.
Let’s begin with the correct pronunciations, namely (listen here and here):
[ˈsmuːð] for smooth, [ˈsmuːði] for smoothie
A very common mistake, is to use the pronunciations
[smu:s] for smooth, [smu:si] for smoothie
with the th pronounced like an s. A good example is the following video:
[smu:s] and [smu:si:] are definitely wrong in English. However, in in German, the Duden suggests to use the English pronunciation for Smoothie.
Another common but incorrect pronunciation is
[smu:θ] for smooth, [smu:θi] for smoothie
with the th pronounced as [θ] (as in think, listen here).
As argued in my previous post, the th is pronounced differently in different English words, and there is no simple rule for a given word. However, in the case of smooth(ie), a good way to remember the correct pronunciation is that the voiced [ð] is a much smoother sound than the voiceless [θ].
Finally, I am having a hard time even understanding the word smoothie in this video, because the presenter is trying to avoid pronouncing the th completely:
The bottom line is: for a smooth pronunciation, you have to pronounce the th in smooth and smoothie smoothly.