tl;dr:When you don't much time to write tests, try this: (1) Generate an output you can snapshot (2) use test coverage to find all input combinations (3) use mutations to verify your snapshots.
tl;dr:Instead of starting from scratch (1) have the new code direct to the old (2) re-implement each behavior on the new codebase (3) slowly delete the old code. Nicolas gives an example of this in action.