Victiours Town League, 1388

During the late 14th century, tempers in Germany flared as town's continued to become even more important. After the death of the Bubonic Plague, princes were short on subjects, and many of them were fleeing to towns. The towns, for their part, resented aristocratic demands on them, physically and financially.

In 137, the Swabian league was formed under the leadserhip of the town of Ulm to stop the Emperor from giving towns to the princes as a way to pay back his debts, and to resist princely attempts to dominate them. The league was joined in 1381 by various Rhenish towns, including Mainz, Frankfurt, and Strassburg.

At the battle of Doffingen, in Wurttemberg, these prineces of Swabia and Franconia, and the Wittelsbachs, defeated them, and the league fell apart.

Suppose they win at the battle of Doffingen? The league already had royal recognition, and a crippling defeat to the Wittelsbachs wouldn't cause the Emperor to shed any tears.

Could we see a state similar to Switzerland arising in Southwest Germany? Or, indeed, joining the Forest Cantons?

Everything is possible, but I consider a union with the Forest cantons utterly unlikely. The swiss attitude was not expansionist at all, and in joining with the rhenish cities they would risk ending up with the short end of the stick.
I would expect that a win by the league would most likely result in a situation similar to the italian city states, in particular if the Emperor recognises the league and there is no evident foe. The league will fracture on commercial issues, and jealousies. Ultimately, they will fall into the hands of some city nobleman.