After the first path led to a dead end due to Metternich's reactionarism the Revolution started us with the second. The person of the king suited for this, since Ferdinand V wasn't much of ruler anyway. The aforementioned Laws of April was signed by him, providing a constitutional basis for the civic changes.
It was fine until the camarilla made Ferdinand to abdicate in favour of his nephew Franz Joseph, and launched the attack to end this little rebellion of ours. The problem was that maybe the Austrian Emperor could just put his crown down but not the Hungarian king. On the basis of the ancient law if you were Hungarian king then you were in it 4life, n keepin it real. A new king had to be elected first, even if it was a formality (it happened in the past that crowned kings elevated an elected king beside them, the heir apparent and they co-ruled), and then he had to be crowned with the Holy Crown during a ceremony with specific rules*.
So it was a possibility to elect Franz Joseph, and wait until Ferdinand dies, then crown F.J. But nor the government neither the Diet were willing to do such things, especially since F.J. and the Court did not want to hear anything about the Laws of April they wanted to restore absolutist rule. From Olmütz he imposed his own constitution on us in early March, which pretty much intended to abolish self-determination, and taking out the control from the hands of the Diet and the government**.
It made clear the Habsburgs won't let us get away with constitutional monarchy, no matter if they remained the titular rulers. So next month the Diet dethroned them and declared independence. Kossuth became the governor, and now we were on the third path. And the fourth. The Declaration of Independence didn't settle the form of government, actually it didn't settle anything. The Laws of April was considered still in effect which implied constitutional monarchy, but our Coat of Arms was changed to a Crownless one, the so called Kossuth CoA, which basically a republican CoA and we didn't have a monarch but a "civilian" at the helm of the country. Many officers were against the dethronement and many more felt aversion toward a republic - smelled too much jacobin and they hated that -, and as before in January this made a particular stratum of the officers and even soldiers feel as they were oathbreakers, and technically this could be held against them (and it was going to). By that time Görgey built up quite a reputation among the fellow officers, he was widely respected, so when he said it's okay, they followed.


*If we really want to be nitpicky we can judge that many Habsburg rulers of ours weren't actually our kings by those rules. Ferdinand V neither.
**On the other hand it implemented modern civic changes, so it can be viewed as path #1. On similar basis the Compromise of 1867 (which given birth to the dualist Austria-Hungary) can be interpreted as a midway between the first two routs, hence compromise.