You could also look at Croatian, which has a similar contrast with e.g. "C", so they use "č" and "ć". This could be easily extended to "s" and "z". Or you could take "ż" and apply the same diacritic to "c" and "s".

"rz" is a bit of a special case since it's pretty much etymological - what used to be "r", and corresponds to "r" in the same roots in other Slavic languages, but became to be pronounced like "ź" in Polish. What to do about it depends on whether you want your orthography to be purely phonemic (a better choice IMO, just look at South Slavic languages - it works great for them!) or retain the etymological distinction. But even then it would be better off as a diacritic.

What would be really neat tho is having a single Latin-based notation that works consistently across all Slavic languages, similar to https://en.wikipedia.org/wiki/Common_Turkic_alphabet. For example, we could use cedilla to represent post-alveolars: ç and ş - and then use acute accent to indicate palatalization ("softness"). So e.g in Czech you'd only need s/ş, in Polish you'd use s/ş/ş́, and in Russian you'd have all four possible combinations s/ś/ş/ş́.

> "rz" is a bit of a special case (...) pronounced like "ź" in Polish

Tiny correction: "rz" is spelled exactly like "ż", while "ź" sounds differently.