... This idea seems like it ought to have been done before. Does anybody know if there's a thread with an idea similar to this one? About a pan-slav country?
I think people have had discussions on this before, but no TLs (It would take a very long period, so would be hard to write it in a chronologically contiguous manner. As many have already said, religion is a big issue, and even when not the real problem, is used to exacerbate it, as can be seen in the Yugoslav Wars and the Polish-Russian rivalry. The only real way to have this possible is either a) have some technological breakthrough early in Russia's history which makes it far more populous, powerful and advanced in relation to other nations in OTL; b) Either get rid of the great schism or make Russia (and Bulgaria, Serbia) Catholic, making religion less of an issue (I just don't see it being possible to have the Croats, Czechs and Poles as Orthodox, even the Slovaks are a bit of a stretch.
You also need to avoid having the Balkan Slavs under foreign domination (or ruled by weaker, more diplomatically isolated powers) which means butterflying away the Ottomans (maybe even Islam in general, although this likely makes Russia have nothing past the Urals or in the Caucasus) and perhaps the Hapsburgs. You might need them as part of a supranational organisation as well (like HRE was to German states). So you see how a good scenario for REAL Pan-Slavism is extremely difficult and butterflies abound. The PoD has to be very early.
(BTW, I am a Slav and a Pan-Slavist, and would LOVE a Pan-Slav TL, but please don't call the state Slavia, it sounds kinda dumb.