Rivers usually don't follow a constant-slope profile; it tends to be more exponential. One 733km stretch on the lower Amazon, for example, drops a whopping 30 meters (it appears to be about two and a half centimeters per km in that stretch), while the upper reaches can literally drop dozens of meters per meter (waterfalls)! The same is true of most major rivers because the river will cut down into its bed until it reaches its lowest possbile elevation (the ocean). Rivers can only cut down if there is a sufficient altitude difference. Once the slope of the river goes pretty flat, it drops a lot of its heaver sediment load and starts cutting from side to side rather than down. It's this side-to-side cutting that causes meanders in the lower reaches of many rivers where the landscape is nearly flat due to early cutting and deposition.
The lower reaches of rivers do tend to be a bit swampy or marshy, but that's usually not a big impediment to enterprising people with sharp axes and pointy plows.
It doesn't take much in the way of elevation differences to make a river run away from what should be a closer run. A small ridge of resistant rock or even a sand bar deposited in times of higher water levels could make a river flow a long way around. It's more likely that the river will find the short path on geologic time scales, but if conditions change it may not have the opportunity to do so.
There are a number of possible explanations for a forest in that position. Glaciers on the high mountains, for example, could feed the river sources. Depending on the intended makeup of the forest, it could be drawing a lot of water from the those rivers. One important considersation is that plants put water into the air. Lots of water. That water condenses back into rain clouds and helps to grow more plants. A forest or grassland tends to be self-perpetuating to some extent.
On the other hand, there is an upper limit on how far water will travel from an ocean. Large continents will have large interior deserts, barring some effect that produces moisture in the interior like a large, shallow sea.
I scale on the map itself would help me in understanding what you're going for here.