Even though x still y sentence pattern
(I'm a native Chinese speaker from Mainland China. People from other Chinese-speaking regions or countries may feel different from me.)

雖然 x 但是 y sounds fine to me for all your examples. 

However, to me the turn embedded in 儘管 x 但是 y sounds a little bit stronger than that in 雖然 x 但是 y. That's why when the conditions are very extreme, 儘管 x 但是 y sounds more natural to me.

I think neither 即使 x 還是 y nor 即使 x 仍然 y is appropriate for your examples.

A critical difference between a. 儘管 x 但是 y, 雖然 x 但是 y and b. 即使 x 還是 y, 即使 x 仍然 y:

For group a, x is a statement that the speaker believes to be true, while for group b, x is only a supposition (usually an extreme one).


  e.g.
  
  儘管我們安裝了最好的安防系統，賊還是進來了。
  
  → The speaker believes that the system has been installed and some
  thief or thieves have found a way inside.
  
  即使我們安裝了最好的安防系統，賊還是會進來的。
  
  → The speaker makes a supposition that (EVEN IF) we installed the best
  security system, and he shows that he believes that still some thief
  or thieves will find a way inside.


Since for group b, x is only a supposition, the sentence below will sound weird:


  即使我們安裝了最好的安防系統，賊還是進來了。
  
  → The speaker makes a supposition that (EVEN IF) we installed the
  best security system, and he shows that he believes that some thief or
  thieves have already found a way inside.