This post is not to recommend any course of action but simply to inform.
Do any state GOP parties have recourse to put on the ballot candidates for president and vice-president other than those nominated in Tampa?
It seems there is (or was) precedent.
In the 2000 general election the Libertarian Party nominees (Harry Browne and Art Olivier) were not listed on the Arizona ballot—the Arizona ballot listed 2 others as the Libertarian candidates. The following is summary coverage of that litigation from Ballot Access News.
Arizona: On September 8, Superior Court Judge Barry Schneider upheld the June 14 deadline for independent presidential candidate petitions. Browne v Bayless, 00-15468, Phoenix. The case had been filed by Harry Browne, Libertarian presidential candidate, on August 18. The day before he had submitted 22,000 signatures (to meet a requirement of 9,598), to qualify as an independent. He had not submitted the signatures on time because he had hoped the ballot-qualified Arizona Libertarian Party would nominate him, but it did not.
The Schneider decision was the first one which upheld an independent presidential deadline in June, since the U.S. Supreme Court victory on this issue in 1983 in Anderson v Celebrezze. Browne cited four precedents from other states which say that June is too early. Judge Schneider did not cite them, and based his ruling on cases from Virginia and New Jersey, both of which upheld June petition deadlines for office other than president. Both states have later petition deadlines for president. Judge Schneider did not seem to know that the two cases he relied on do not relate to presidential elections. The Supreme Court had said in Anderson v Celebrezze that states have a diminished interest in keeping presidential candidates off the ballot, than candidates for other office.
Browne appealed to the State Supreme Court, making sure there would be no confusion about precedents this time. However, on September 12, that Court refused to hear his appeal (no. cv-00-327-SA). Browne then filed a new lawsuit in federal court. Browne v Bayless, cv-00-1774-PHX-RCB. However, on September 22, U.S. District Court Judge Robert Broomfield, a Reagan appointee, rejected the case on jurisdictional grounds: (1) the federal court cannot take jurisdiction while it is still technically alive in state court; and (2) the case should have been filed sooner. Broomfield’s opinion is 32 pages long and is of far greater quality than the state court decision. It acknowledges the precedents from other states on June presidential deadlines, but never reaches a decision about the constitutionality of the Arizona deadline.
The constitutional issue will be pursued in the State Court of Appeals after the election.
Obviously, each state party organization has bylaws as does the National GOP, and each state has relevant ballot access laws.
May a state GOP organization be compelled to accept a ticket its members don’t want?
It does seem to be an open question. We don’t have information about any additional findings in the Arizona litigation.