Thanks to everybody who replied to this specific question!

In particular, John Cowan scripsit:

<<Well, we can use plain [s] for the apical version, Basque /s/, and
add the "_m" diacritic for laminalization (U+033B COMBINING SQUARE BELOW)
for Basque /z/, since there is no diacritic for apicalization.>>

As Christophe mentions below:

<<[s_a] in X-SAMPA. In IPA, you add a small rectangle with the top missing
under the consonant.>>

I consulted the charts and indeed found a diacritic U+033A COMBINING
INVERTED BRIDGE BELOW. It's never too late to learn!

Danny Wier agrees, saying:

<<Euskara /s/ is usually rendered as s with the apicodental bridge
(a [ turned 90 degrees to the right); /z/ is simply [s], being alveolar.>>

whereof I highly doubt that /z/ is *alveolar*. For my Russian ear it was
definitely *dental*.

He also says:

<<Dravidian languages have dental vs. alveolar distinction: Tamil has /n/
/n_/ and /r/ vs. /r_/ (I'm not sure of the exact pronunciation).>>

Thank you, Danny. I knew it. Neither am I sure of the pronunciation :-)
Still the examples shaw that having oppositions inside the "front-tongue"
PoA is quite naturalistic.

ObConlang: To know the answer was really necessary for pinning CLP-6
("Caucasoid") "front-tongue" (using Russian terminology) fricatives. Now I
can describe them as /s/ [s_d], /s_a/, /S/, /s`/ and their voiced
counterparts :-) Stops aren't so evil, having only binary opposition /t/
[t_d] :: /t`/. I was shocked to see a similar system in Toda language
mentioned in Peter Ladefoged's Course in Phonetics