I note McCree turned sixty in 1980, and it sounds like his health was poor in the years up to his death; it's possible Marshall could retire in 1983 before the election year, when presumably McCree would be considered too old, and Higginbotham would have six years on the appeals court under him.
It's sort of interesting that Higginbotham might just retire in 1990 or 1991 the way Marshall did, since Higginbotham retired from the Third Circuit then. He was diagnosed with some sort of disability. But Higginbotham was still doing private work until his death in 1998 I think, so he could hold out more easily than Marshall could or would if he didn't like the incumbent president who might appoint his replacement.
Marshall and Brennan OTL absolutely had issues with the President who was replacing them. They'd held out for over a decade under Reagan and then Bush before throwing in the towel.
The 1984 Republican nominee, no matter who they are, will be somebody who is either Conservative themself (Danforth, Dole, Kemp, Laxalt) or will have to shore up the party's Conservative flank (HW Bush). Think of how Ford needed to make Dole his VP in 1976 - by this point Conservatives had to be taken into account. It's also worth considering that even the moderate Republican Presidents like Eisenhower, Nixon, and Ford weren't
trying to nominate moderates or liberals, there just wasn't yet the same sort of vetting process that came later. Even HW had that issue. Bork was a finalist for the Douglas seat that went to Stevens, after all. Nixon was somewhat disappointed with Blackmun and Powell.
If seats open up in 1986 (Burger) and/or 1987 (Powell) there's the issue that the Conservative Republicans don't have much of a bench though. Look at OTL names from the Reagan/Bush period (1986 to 1991):
Antonin Scalia - head of OLC from 1974 to 1977 (which itself was where Rehnquist was plucked from) but put on the DC Circuit in 1982.
Richard Posner - put on the Seventh Circuit in 1981
Doug Ginsburg - Regulatory Czar in 1983, DOJ 1985-1986, DC Circuit 1986 ... and also nominated partly out of spite after the Bork failure (Reagan wanting to put somebody younger and possibly more extreme than Bork up out of spite). He had the advantage of being a Thurgood Marshall clerk though.
Lawrence Silberman - DC Circuit 1985. Before that he had various Nixon/Ford-era big legal posts like Solicitor of Labor, Deputy AG, and acting AG briefly. He also had lots of private practice experience.
Frank Easterbrook - Put on the 7th Circuit in 1985. But he'd been in the Solicitor General's office too (arguing 20 cases before the Supreme Court) and was promoted to Deputy Solicitor General
during the Carter Administration.
If the emphasis is on judicial experience (preferably more than just one year) ... you've maybe got the Conservative Arlin Adams on the Third Circuit or the moderately Conservative Anthony Kennedy out in the Ninth Circuit (there since 1975).
If you're looking beyond having enough experience as Federal judges (which Reagan sort of did when he picked O'Connor, although she'd been an intermediate-level state court judge for a bit) Orrin Hatch and Robert Bork are understandable picks. Silberman or Scalia or Easterbrook, with their prior executive branch legal experience, all could work since just a year or two of judging would be on top of otherwise sufficient legal careers. Ken Starr clerked for two years for Burger.
If Jack Danforth is elected President in 1984, Clarence Thomas might get put up. Danforth was Thomas's big booster OTL. He was assistant AG for Missouri from 1974 to 1977 under Danforth, then joined Danforth's staff in Washington in 1979 (a legislative assistant for the Commerce Committee) - only leaving because Danforth recommended him for a post in the Reagan Administration. He would probably get a more important posting than he historically did in the Reagan Administration, and that could be a pedestal from which he's moved to the Supreme Court in 1986 or 1987.