Solving OID wrap-around in 7.4 DB?

On behalf of a previous employer who, due to major downsizing, is left
without an answer to this:

What's the best way to treat impending OID wrap-around in a 7.4.8
database? This DB has been online for about 18 months, and is expected
to hit the dreaded wrap-around in about a month. At an application
level, there's some small chance that OID wrap will cause failures:
there's code that writes rows, and (for tables without primary keys)
relies on DBD::Pg's pg_oid_status method to identify the last INSERT.
(The vast majority of the code does not rely on this, but there's a tiny
fraction that does, and rewriting the code to remove this is not an
option due to the aforementioned downsizing.)

My immediate take on this is that the only sure way to avoid the problem
would be to dump and reload the database. Due to the size of the
database, this is likely to take most of a day. Any other options?