I wouldn't make an assumption about the gray water discharging separately. I know people who have brand new houses and discharge gray water separately albeit not within the confines of the law. The fact of the matter is that it is soapy water and it'd be hard to argue that it is any more harmful to the environment that washing your car on your lawn. I am assuming that the toilet in the basement is still routed to the septic system since you obviously wouldn't want to discharge solids onto your lawn.
It sounds like the system hasn't been maintained and more specifically pumped recently but that doesn't mean that it is undersized. Regardless of how large the tank or field is, if it isn't ever pumped it will fill up. I assume this is a traditional septic with a leach field and not just a holding tank. Also unless the system is backing up or otherwise failing discharging the gray water to the tank will not fill it up any faster as the gray water will leach out into the field (in the case of traditional septic) or be pumped to the mound (if it is a mound system). The same goes for rain water seeping in. Only solids remain in the tank so any additional water just minutely increases the wear and tear on the leach field (in the case of tradition septic) as well as the frequency of the pump running (in the case of a mound) and that is why some people (illegally) choose to discharge gray water onto the lawn instead of running it through the septic.
From what I hear the only thing that needs to be done is to reroute the basement gray water to the septic tank and have the tank pumped and you should be fine. The lack of diligent maintenance could be of some concern but if the septic isn't backing up or otherwise showing signs of failure I wouldn't personally be all that concerned about it.