There is no reason to feel scummy

You are giving the children exactly what they need. A loving home. I consider myself blessed for having made your acquaintance.
Look at it this way, would it be “better” to let them do without a medical/mental treatment, because you can’t afford it? Or because you feel “scummy?” Would it be better for the other children in the family to ‘do without” while you pay for their treatment? The answer is NO! Your job, as the good parent you are, is to make certain ALL of your children the best loving care you can and if getting assistance in doing that is required then you do it.
You pay taxes right? In fact there will be taxes taken out of any money/treatments they might receive. So why do the children not deserve the financial/medical/mental help?
As for future implications on their rights, only ss can tell you that. Getting them help now might actually help them because it will give documentation of the problems they have had all their lives.