The Texas legislature is discussing whether to move the state’s primary from March to April. See this story. Senator Leticia Van de Putte (D-San Antonio) would like to amend her SB 100 to make this change. SB 100, as introduced, only concerns procedures for absentee voting, but the bill could be amended to revise the primary date. If the legislature moved the primary from March to April, that would automatically mean a later petition deadline for minor party and independent candidate petitions, for office other than President.
Other bills that might serve as vehicles for the primary date change are HB 111 and HB 3585, by Representative Van Taylor (R-Plano).
Texas currently has the earliest petition deadline in the nation for independent presidential candidates. Unfortunately, the independent presidential petition deadline is not keyed to the date of the primary, so if the primary is moved to a later date, that would not improve the independent presidential deadline.