On April 2, the Oklahoma House Judiciary Committee passed SB 668 unanimously. It has no effect on the number of signatures needed for a newly-qualifying party in presidential years. But it lowers the number in midterm years, so that if the bill becomes law, the two types of years will have an equal signature burden (5% of the last gubernatorial vote).
The bill is now three-fourths of the way through the legislature. Thanks to E. Zachary Knight for this news.