(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).
→ The speaker believes that the system has been installed and some
thief or thieves have found a way inside.
→ 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:
→ 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.