My proposal: Ladislaus V is healthy and doesn't die in 1457. He spends the first few years of his reign crushing the Hunyadi League and restoring royal authority. He could further strengthen his position by marrying a surviving Garai Anna. With the lands of the country's three most powerful families at his disposal (Hunyadi, Garai, Cillei), noone could pose a threat to his rule.
Around 1463, Ladislaus participates in the crusade initiated by Pius II and leads his united Austrian-Bohemian-Hungarian armies against the Ottoman Empire. Other notable participants of the crusade are the Papal States, Venice, the League of Lezhë(Skanderbeg), the Despotate of Epirus, Stephen II of Bosnia and (the exiled) Vlad III of Wallachia. Frederick III Holy Roman Emperor also provides some support.
During the crusade, the Habsburg army quickly takes (the just recently fallen) Smederevo and heads South along the Great Morava, while Skanderbeg (reinforced by Papal and Venetian forces) marches through Kosovo. The two armies merge near Skopje, just in time before the arrival of the Ottoman main army. The Battle of Skopje results in Christian victory and the Christians occupy the city. This marks the end of the campaign of 1463.
In the next two years, the Christian forces act separately, since they only have to deal with local armies. In 1464, Vlad III gets restored in Wallachia, Habsburg and Bosnian forces clear out the remaining Ottoman presence in Bosnia and Moravian Serbia (most notably with the conquest of Golubac), Skanderbeg secures Ohrid and South Albania and the Venetians take Valona(Vlorë). Around the end of the year, Ferdinand of Naples also pledges support to the Crusaders.
In 1465, the Crusaders continue their advance. The Wallachians take Giurgiu, the Habsburgs take Vidin, all of South Epirus gets restored to Epirote rule, but most notably Morea gets restored to Palaiologos rule. The decisive battle of the war is fought in 1466, when Ladislaus V and his allies' forces clash with a new Ottoman grand army led by Mehmet II. The battle takes place near Silistra and once again results in Christian victory. Christian conquests continue in the next year, but there's an ever-increasing war-weariness among the participants of the crusade. The last major achievement of the war are the fall of Sofia to the Habsburgs and the Venetian capture of Thessaloniki.
The Peace of Adrianople(1467) officially ends the war between the Ottomans and the Crusaders.
The new borders would look something like this.
Imo this is the max extent a single war could possibly take from the Ottomans in the 1460s. Furthermore, much of these losses could be rather easily be reversed.
So, realistically speaking, something very bad would need to happen to the Ottomans in Anatolia for the Balkan Reconquista to become fully achievable within this century or the next. Alternatively, these Balkan statelets and their neighbours would need to replicate this same level of cooperativeness, vigor and success atleast two more times.
A single large-scale Pan-European crusade could also do the trick, but chances for such thing to occur are even more slim.