First off, sorry, but i love these sorts of threads because it gives me the opportunity to plead and beg for Basque
Basque is a language known for being grammatically complicated, but it's surprisingly regular and despite having a lot of cases they all follow very simple patterns unlike Russian or German where you have to worry about the gender of the noun (no genders in Basque) or whether it was preceded by a definite/indefinite article, etc. And unlike many other European languages, you only need to worry about declining the last word in the phrase (so no coordination like Spanish's lOS altOS techoS or German mit dEN altEN bücherN).
The main difficulty with Basque is the verb system, and not because it's highly irregular like English or Spanish which have a number of irregular verbs but because the verb contains so much information. Basque verbs are basically like a puzzle where you have to pick the pieces (subject, object, and direct object) to form the final verb. In fact, most Basque verbs aren't conjugated at all, they use an auxiliary verb (similar to "have" in English's "I have seen it").
I think the structure of the language is very suited to the SSi method and would work realllly well for it. Euskaldunak tend to be very proud of their language and are really excited about sharing it with others. After all, the Basque word for a Basque person (euskaldun) literally means "one who has the Basque language" (ie. a Basque speaker). They only differentiate between euskaldun zaharrak ("old" Basques) and euskaldun berriak ("new" Basques). That idea is really interesting to me, more important than national boundaries, so long as you learn the language you will be accepted into the culture and can become a "Basque".
Welsh is super lucky to have SSiW, i think people trying to promote a minority language need to realize how important audio courses are. I've been working on getting various resources out for Basque for a while now and have been working on an overview of the main grammatical features that a course intending to take someone from a beginner level to competent speaker would need to cover. But what Basque (and many other minority languages) is sorely missing is an on-the-go portable audio course that can get you actually speaking the language. Because that's what we want after all, isn't it? For people to actually use the language in their daily lives!