Framing the developments in Hungary as a "Hungarian Revolt" is a gross mischaracterisation. Until at least October 4th, the Hungarian side didn't commit any anti-constitutional act. The earliest act that could be described as treasonous was when the Hungarian army crossed the Leitha (the Austro-Hungarian border) on the 28th of October, then attacked the forces of Windischgrätz at Schwechat. Still, considering that the Court began to actively endorse the rebel Jelačić (and Windischgrätz united his forces with his), the Hungarians were hardly the ones solely at fault there. In fact, despite the circumstances, the Hungarians tried to stick to legality for a very long time, and fought in the name of King Ferdinand V against the "usurper" Franz Josef all the way until 1849 April 14th (when Kossuth hijacked the legislation and forced through the "declaration of independence" and the dethronement of the Habsburgs).
To prevent the situation in Hungary getting out of hand, I propose the following scenario: Count Lamberg doesn't get recognised on the streets of Pest and doesn't end up getting killed by an angry mob. Within a few days the latest, the meeting between Prime Minister Batthyány and Count Lamberg takes place. Lamberg receives Batthyány's ministerial countersignature for his appointment as Chief Commander of all armed forces in Hungary and provisional Palatine. By this point, Jelačić is already beaten at Pákozd. In hope of receiving support from Austrian War Minister Latour, Jelačić declines to negotiate with Lamberg and the Hungarians and withdraws in the direction of Vienna. Without the OTL shock from Lamberg's death however, the Court in Vienna doesn't stand behind Jelačić, and once the news of Pákozd reach Vienna, he also falls from Latour's favour. At this point, Jelačić attempts to return to Croatia but the Hungarian army catches up to him and decisively defeats his army. The strong Hungarian position allows the successful conclusion of the negotiations concerning Batthány's new government formation, and the situation calms for the moment.
This has some interesting ripple effects. Without Jelačić's appointment as Chief Commander/Military Governor of Hungary and Latour's order to reinforce Jelačić's forces, there's no revolution in Vienna on October 6th. The Austrian Reichstag also would remain in session in Vienna. It is also more than likely that Johann von Wessenberg-Ampringen would remain the Austrian Minister-President for the time being, keeping Schwarzenberg out of the picture. All in all, this also prevents the abdication of Ferdinand I/V, which keeps Archduke John in a powerful position as Viceroy of Austria. Without Schwarzenberg's demands for the admission of "all of Austria" into Germany, the pro-Austrian faction remains more popular in Frankfurt, which also means that Anton von Schmerling remains the German Minister-President.
Without the turmoil in Vienna and the erupting open conflict with Hungary, Princess Sophie's clique would be in a far weaker position and would be unable to force Ferdinand's abdication like they did IOTL. As such, arch-conservative and reactionary forces would remain to be forced working within the new frameworks and combat the liberals and reformers in such context.
All of this could eventually develop into the proclamation of Germany under Habsburg hereditary imperial rule, although it would be Ferdinand to whom the imperial crown is offered, not Franz Josef.