Cheap and not really usefull irony aside, the big problem of the Hungarian is that they are not really friendly with the other ethnicities at the end it come to a choice between them and the others as any increase on the right of let's say croats will have not taken well in budapest. Deal with the hungarian nobility as soon as possible and at least you can try to work some agreement with the other parts, keep things as they are and you will fight an uphill battle even for the slightest modification.
Im not saying that the hungarians werent a problem or even the biggest hurdle if you wanted to federalize the Empire but there were also other, incredibly hard to impossible to solve to the satisfaction of all sides problems. Take the second biggest one: What do you propose as a solution to the czech question? Look at the demands of the czech nationalist and tell me a solution thats acceptable to both them and the germans? Because I really cant.
Further if you wanted to rank the nations of the Empire in terms of importance for the survival of the Empire IMO that would look like:
Germans - had money and positions, the core of the empire
Hungarians - had money and positions, fully in the Empire, no unsolvable disutes with the most important nations
Czech - had money and positions, fully in the Empire but a nearly impossible to solve dispute with the germans
Croats - had money and positions, fully in the Empire serious but IMO not unsolvable dispute with hungarians
Poles - had positions and some money, hard to solve dispute with Ukrainians, also unreliable in the case Poland ever gets its freedom
Slovakians - no money or positions, but at least fully in the Empire, unsolvable dispute with hungarians
Slovenians - AFAIK no money or positions, at least fully in the Empire, very hard to solve dispute with germans
Serbs - no positions but some money, not reliable because of hostile Serbia on the other side of the border
Romanians - no positions but some money, not reliable because of Romania on the other side of the border
Ukrainians - AFAIK no money or positions, but more reliable than the above two
Italians - few and unreliable because of Italy on the other side of the border
I admittedly know much less of the austrian affairs than the hungarian ones.
The point im trying to make is that if you want the Empire to survive in the long run you have to get at a bare minimum the germans, hungarians and czech on board. It would be a huge bonus if you could also win ower the croats and/or the poles. A military solution against the hungarians will alienate them, and you will do so in big part to win ower serbs and romanians (who are hard to rely on because of their national state on the other side of the border), and slovaks (who have neither the money nor the education to be of much use initially).
Further and most importantly look at the situation in Hungary before the war:
there was very little pressure on the hungarian leadership to even consider a change. There was little internal pressure: there were no mass rallies by the national minorities, or even terrorist actions or anything. They were also barely present in pairlament. The socialist caused more trouble than the minorities to the government.
There was little outside pressure: Neither the austrian side nor the Emperor was pressing the hungarians to accept any change of the Empire.
The hungarian elite is often portrayed as blockheads absolutely refusing to change. They had no reason to - there was very little pressure on them to do so. There is little reason to suppose that this would not change if there was serious pressure put on them to accept a change - like FJ dying and FF pushing for changes as Emperor, or the natinal minorities in Hungary becoming much more active politically in or outside of pairlament.
I also want to point out that the idea that the problem can be solved by getting rid of the hungarian "nobility" - lets say elite, supposes that unlike any other nations in Europe at the time the hungarian common people who did not have the vote were not nationalistic and be fully ready to sign away most of what they saw as their country. That I consider as incredibly naive.
Personally my opinion is that most people who want a surviving Habsburg Empire do so by going for an easy solution that IMO would not work because it completely fails to consider that the Empire was an incredible complex mix of nations, rivalries and interests. Untangling all of that in a somewhat workable form.... The only workable way forward in such an environment would be a huge amount of compromise on every side reached with tons of diplomacy, which is inredibly hard to do, requires a lot of patience and might be just impossible even with that. But people want to move forward with their ideas and timelines, and not dwell on some of the most complex issues of the time. So they go the easy way - blame it all on the hungarian elite, the forcefull removal of which will magically solve all the problems of the Empire and have everyone else be happy to set aside their grievances and differences, and create a new imperial federation...