On the evening of March 16, the Oklahoma House passed HB 1615, which moves the primary (for office other than President) from July to June, and which also moves the deadline for the petition to create a ballot-qualified party to from May 1 to March 1. The same bill, SB 602, had passed the Senate on March 8. Therefore, the idea has effectively passed the legislature.
The bill also says that a group must have started its party petition in the odd year before the election. Oklahoma requires that groups give notice when they begin to circulate the party petition, and the bills say this notice cannot be given during an even-numbered year (except very late in that year, when the petition would be too late for that election year).
Meanwhile, HB 1058, the bill to lower the number of signatures for the petition to recognize a new party, has not moved since it passed the House Rules Committee. It will probably receive a vote in the House on Thursday, March 17. It must pass the House on March 17 or it is dead. Since this is the deadline for House bills to pass the House, the House is expected to be in session until late into the evening.