Do we need to dump the existing rafters and install a roof with a
steeper pitch or is there a way to reuse the rafters that we have?

You should not be depending on the snow sliding off your roof
to keep it from collapsing, no matter how steep a pitch it has.
If your roof won't support the expected snow-load, then
re-enforce it. You can do this by doubling up the rafters,
or putting in a support beam (purlin) mid-span, or any number
of other ways, only one of which involves taking the roof
completely apart and re-building it from scratch.

--Goedjn