All divisions of Slavic languages based on phonological criteria that I have seen so far are rather minor and/or localized (e.g. spirantization (Czech, Ukrainian) or not (Russian, Polish) of g). Is this indeed the case? Or am I missing a major partition that can be done based on more solid/systematic phonological aspects? (such as the La Spezia-Rimini line.) There is, of course, the retention of tone in parts of South Slavic, but it doesn't seem to be in the same league of relevance as the LSR line.
The main classification of Slavic divides it into South Slavic, West Slavic and East Slavic.
The most important partition of Slavic languages is the band that separates South Slavic from the rest of Slavdom, cemented by the establishment of the Magyars in Pannonia.
But there are features shared by South Slavic and East Slavic but not West Slavic, and important isoglosses within South Slavic, many involving yat. South Slavic is a dialect continuum but not provably a phylogenetic clade. That is, there were multiple waves from different places in the North.
It's not like the La Spezia-Rimini line, it's more like the break in the continuum between Daco-Romance and the rest, including Italian.
While the La Spezia-Rimini line explains some interesting features, they're a small subset of the total features. Parisian French is non-pro-drop and has extreme phonological innovations, so that Spanish and Italian - based on dialects just southeast of the line - are more similar to each other on many important dimensions, and arguably overall.
The mutual intelligibility between Daco-Romance languages, like Romanian, and the rest of the Romance world - even southeast of the line - is severely affected by a millennium of geographic and cultural separation, substrata and so on.
Concretely, are we really sure that no Roman from southeast of the line ever went to Iberia? In fact, we know they did.
Note that this is a political map, and therefore oversimplified.