I'm aware that it's possible to sit for the bar exam in some states after a foreign LLB/JD provided you complete an US LLM.

However, I've checked the admission criteria for some US LLM programs and it doesn't seem as though they are willing to accept students with a LLB/JD completed via correspondence or distance learning (so California DL schools seems to be out too...). Anyone know of any schools that don't have this criteria?

I cant say for sure, but Washington doesn't appear to specify the type of education for non-US lawyers, but apparrently requires admission to and experience in a common law jurisdiction

http://www.wsba.org/Licensing-and-Lawyer-Conduct/Admissions/Bar-Exam-Admissions/Qualifications-for-Bar-Exam