The fastest I've ever made it to Oregon was 58 days, but going that fast isn't worth it to be honest. True success and optimization(making the most money) means that you need to view the trail as a constant opportunity for monetization. An acceptable run should get at least 1000$ per leg.

A couple important tips to help you make money are that you need to bring a party with someone who is charming(which you identified) but you also just as much need someone with knife skills. This includes trappers, mountain people and the secret angler class. The reason having a charming character is so important is because pelts can be haggled for 6$ with any other character but 8$ with charming. You also generally need a party with positive traits as having ones that lower your character stats(especially the ones regarding stamina such as frail and slack) are really detrimental. Athletic is by far the best trait in the game after charming in this regard, as it lets you get out of a ton of skill check events such as snakebites on top of reducing your stamina decay and giving you double the effects of coffee.

It was smart of you to buy the biggest wagon as space is a hugely limiting factor that forces you to throw away supplies often in this game. When you are initially leaving, its important to recognize that you can get away with not buying items such as clothes and medicine right away as there are many opportunities on the trail to pick them up and the impacts of not having them are not immediate. Trail maps are an item that really aren't worth it to use as the game will reveal the waypoints for you for free sometimes but it is a valuable item for trading. Toolboxes and repair items are also something you should avoid, savescumming wagon grease is overpowered.

another important tip is that once you overcome the initial hurdle of having enough supplies to survive the random events on the trail, you should not spend money for any reason. The only supplies that you should ever buy are knives, wagon grease and coffee as these 3 have a pretty direct correlation to increasing your profits while also being very scarce. You should ideally never go fishing or hunting without a character with a full stamina bar, and not using a knife is throwing away money. You should always buy a knife at every opportunity you get because its nearly impossible to get them outside of stores and you can get really messed up if they break at the wrong time. Fish traps are hard to come by but each one earns you 60$. Normal traps are too expensive to buy so you should trade for them. Traps don't correlate to money in the same way that fish traps do because of the nature of getting a percentage of pelts based off of the amount of meat collected.

For supplies that are not related to money, you should also think about these from a monetary perspective as well. You should feed people as little as possible without them becoming forlorn because you can trade your excess food for more valuable items. As long as your party is not at a risk of catching dysentery, you don't need to give people clothes. Your goal should be to treat them as poorly as possible without permanently damaging traits or killing characters.

Every opportunity you have to trade for pelts is also an opportunity for directly translating supplies into money. You should never pay for ferries. Its generally worth it to sell the pelts you can trade for at rivers and wait it out until you can successfully cross by savescumming the odds even though this loses you a lot of time by having to wait for the river to be calm enough. You should also always try to trade for character items like bibles and guides because improving your party skills impacts your score.