Why bother with a check valve? If you have a blocked downstream pipe,
you are going to get a backup out through something no matter what you
do. Would you prefer having waste water spill out your kitchen sink
rather than out a washing machine drain in the basement. In your
current setup, if you have a blockage near the septic tank (yikes, only
a 1 1/2 drain running outside! Does it freeze where you are?), your
existing washing machine drain would overflow too, right?
Even in a house plumbed perfectly to code, there is no way to avoid
having blockage cause overflow at some fixture -- usually the lowest
fixture above the blockage. I suppose you could add a check valve on
every fixture, ... which would accomplish exactly nothing useful.