I have enabled a way for those reaver with absolutely nothing better to do to
make reaver quests save over reinc. Nothing will ever save them through
rebirths.
This requires a MASSIVE energy drain, so much so that only Ultimate reavers
can even attempt this. The 4th layer reaver guild room contains more useful
information about what reaver quests/tours you can save. Hopefully it will not
bug.
Note that a couple of the reaver quests are completed by spite data. These
save because spite data is not cleared at reinc. As such, making those
permanent is probably not your first priority, but you can always do it for
show.