Effects of a shorter of Battle of Sevastopol on the duration of the Crimean War

The Allies missed a number of lost opportunities to end the Battle of Sevastopol early on during the fighting (for instance, they managed to set off one of the Russian powder magazines, which destroyed one of the major redoubts in the Russian defensive line, but didn't end up pressing their advantage). Presuming that the Allies capitalize on an incident like the one mentioned and are able to seize the city and its defenses without months and months of tedious investment and high casualty siege/trench warfare, would the shock of the decisive defeat bring the Russians to the negotiating table any quicker than IOTL?
 
The Russians would definitely come to the peace table at once as you surmised, but the allies-mostly the British under Lord Palmerston-would call for a more concentrated effort on another front namely, Russian positions on the Baltic:Finland, Aaland Isles, Estonia & Lithuania and Ingria.
The key to which would be the Fortress of Kronstadt and St. Petersburg.
So it could be possible for a more expansive and longer war strecthing beyond the Caucasus and Crimea, but this is all depending on how Britain and its parliament would agree with Palmerston who had already devised extensive strategies and campaigns for such a measure and it could see the French either making a seperate peace and letting the British on thier own or a direct prevention of such actions by the French during negotiations.
 
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