It sounds like you are certain that the problem is isolated to just the window. If the drains are working, but water accumulating in the channel, faster than going out the drains, you need to figure out why. Does the window not fit properly? If no obvious reason, I'd start by removing entire window/frame, and reseal behind frame, reinstall window/frame. Removing the window, may require a helper, but not a hard job.
Never overlook a possible point of entry above the window.
A mobile RV tech would be a good option, if you don't want to tackle this yourself.
Jerry