Ha ha... Their chances aren't good.
You see, the problem with rebelling against the king while having 6 months of spare time is that there's a good chance money won't save you, let's look at this from certain aspects that tie in directly with economic factors:
Military. You rebelled against the king and did things that will get him, all of his nobles and all of their noble's vassals against you. Not because you're taking the king's land, but because you preemptively attacked nearby nobles and is clearly agaisn the system they run. In other words, you're a threat (especially for the nearby nobles) and needs to be trampled ASAP to ensure stability to the system. This means that the chances of the king not being able to gather a decent military force as soon as possible due to nobles deciding not to join in are slim, because you've shown every member of nobility you might go for them next if you feel like they're a threat. Furthermore, you have to build an army from the ground, with only your townsfolk and the peasants to serve as soldiers. In this scenario, money isn't the problem here, time is, because you'll most likely be outnumbered and can't afford to waste any chance of getting more well trained ground forces. Proper military forces take time to train, especially regarding more elite positions such as experienced bowmen and professional knights (both of which were normally trained from a young age), which require both a grater sum of money and many more years of training to be made than your "disposable" peasant Frontline soldier with only enough training on how to not kill himself with his spear (which is also why loosing a bowman or a knight was normally bad, they're not easily replaceable and chances are you can get a ransom for them, at least regarding the knights). Your best bet now is finding trained mercenaries to make a private army, much like kings started doing near the end of the medieval period. If mercenaries are not an option, you'll have to stick to some good guerilla tactics to have any chance, because it'll be a bunch of poorly trained soldiers against a larger, more well trained and potentially more well equipped opposing army that likely doesn't plan on leaving survivors.
Political. You know how the stock market can fall in a country experiencing internal turmoil? Same here. The king and his nobles may need 6 months to begin assembling their forces, but letting their territories know that anyone who trades with the rebels will be banished as traitors at best and hanged at worst takes a lot less time. Merchant guilds might avoid trading with your city now, because there's a decent chance they'll face retaliation from nearby powers, both physically and economically speaking. If the nearby regions aren't ruled by idiots or stereotypical evil movie nobles with only half a functional brain thanks to inbreeding, there's a chance they'll try to use their available political, military and economic power to begin strangling the city before engaging it. They need to make an example out of you after all.
Social. There's a good chance your city will rely on peasants in a way or another, because trading will most likely be affected and nobody unwilling to piss the king and the nobles off will want to associate with your city. Come in the peasants: as far as your description goes, it doesn't seem like the peasants had a lot of participation in the decision-making of the whole thing. As far as it might seem, you're rebelling against the king and nobles and then trying to drag them into the hole with you. There's also another problem: sure, they'll live rent free an only be bothered when they need help with construction or military matters... such as right now, right after you've began taking down the nobles, which is the only reason you need them to help you out at this moment anyway.
Furthermore, unless you show them your well paid mercenary army chances are that all they'll see is a prideful city trying to rebel against the nobles and the king while asking them to join their fragile cause, one which lacks the proper military power to back it up.
Religion. The entire situation becomes extra bad if your medieval world has similar relations with religion like some European countries had with catholicism, because the church can stand even atop the nobles in certain cases (being considered as above them in the hierarchy since they save everyone's souls), as nobody wants to go to hell. In such a scenario, if the priests don't side with your rebellion and say you're being controlled by the devil, chances are that neither will the peasants, especially if you respond to such words by doing to the priests what you did to the nobles. Now the city would have reduced trading, reduced food availability, every member of nobility out to get them and a mob of angry peasants trying to end them.
Security. Remember why feudal relationships came to be in the first place? With how invasions and pillaging were happening left and right? Well if your world also has that you'll need to worry with yet another problem, and the existence of such invasions would make proving to the peasants you can protect them as well as the previous nobles even more important, because everyone wants to go to heaven, but nobody wants to die unless there's something in it for them in the afterlife.
So summing up, here are the problems I see as most important:
you've angered the system itself with your actions and will most likely be outnumbered (don't believe me, see the French revolution an how every other absolutist country nearby wanted it to be over by yesterday at the time).
you have very little time to train an effective military force (and that's taking in account that normally peasants had nearly no training, because you'd be better of exploiting that in the enemy forces), and your situation as a single city once part of the king's domains means you can't depend on a victory through sheer numbers. You might have to use a good portion of the money to pay mercenaries to fight for you or at least bulk up and strengthen your forces while convincing them that trampling you, stealing your gold and handing over the region back to the old nobles instead isn't a better business (remember, Mercenaries fight for money, and depending on their morality, money will be important to ensure they remain reliable and loyal to you).
trading might be affected since you're now most likely marked as rebels by the majority of the big figures (and their respective regions) nearby.
you need the peasants to believe your revolution will be better for them than the old system while proving you're just as capable of offering the same benefits the older system did, such as protection.
if religion is an important part of everyone's lives, especially in case of the peasants, you'll need every nearby priest on your side to prevent groups of peasants from rising against your revolution, and if religion doesn't side with you, trying to persuade them through force will likely make the situation even worse.
if invasions are a thing, there's a chance that you will need to be capable of dealing with them and the king's forces.
there's a risk that the king and his nobles will send assassins to get rid of the revolution leaders in the meantime. Murdering the leader is a fairly common strategy.
All of these affect the economy, because depending on how the peasants, the church, the nobility and the traders see and treat you, you'll need more or less money to make it all work, with a worst case scenario where not even all of the money might not be enough to solve the situation in a favorable way for the rebels.
Also, it might have been obvious already but your social experiments has to wait. 6 months is not a lot of time to go from a large trading city with nearby peasants to a military nation with some properly established defenses and troops, and depending on how similar your medieval world is to our own, you're already behing schedule in terms of what needs to be prepared. Your city is in the place of France during its revolution, meaning everyone wants your revolt trampled, your rebels publicly hanged and their associates dead.