There are three ways to beat the debt I know about, I haven't played the newest version yet though I have wanted to just have had other things to do.
The method I've used before is to focus entirely on resource collection starting with fishing, then unlocking woodcutting, stone, ore, and smithing in that order and only acquire new slaves when you have something for them to do trying to get ones that like fish. Sell all but the food you need to keep your household fed and all resources you gather that aren't being put towards upgrades, doing this I was able to finish the entire 100k debt around day 60 of 100, a few of the early weeks might be tricky but should be easy enough once you get past them. While doing this I also ignored 90% of the guild quests and only started combat excursions once it was impossible for me not to make the cash goals.
The second method would be as vadi says, rush reputation as fast as possible to advance the main story and get the debt "frozen".
The third method I've heard people try but haven't attempted myself is to focus on combat, not sure the totality of that strategy.