Although the highway A-20 ends between Cacouna and l'Isle Verte, there is also a short bit of it around the city of Rimouski. This can be helpful if you are heading West, but is more tricky if going East.
Going East by highway A-20 is not so easy, so you might want to try reaching the §rd Rural Route (3e Rang) via the Chemin du Sommet.
Going West, Rivière-du-Loup, Quebec city
The best hitchiking stop needs you to walk a bit but is safe and quick: there is a ramp for highway A-20 at the corner of Montée Ste-Odile and Boulevard Arthur Buies. From there you easily get a ride at least to Le Bic. If you are dropped there, simply hitch again at "Le restaurant du Pecheur" where a lot of people stop and the parking lot entrance is very large.