politics

There are a few ways to reform the court without a Constitutional amendment:

• Increase the number of justices on the bench. The Constitution sets no limit or requirement for the number of seats, only the process by which they are filled. Nomination comes from POTUS and will need to be "consented" to by the Senate. The number of seats has changed in the past and will change again, just a matter of when and who stuffs the court.
• Establish bounds of "good Behavior" and define means of removal. The Constitution isn't very cut and dry on the removal process of Justices (with impeachment being reserved for the "President, Vice President, and all civil Officers" the latter group being left undefined), but it does say that the Judges shall "hold their Offices during good Behavior." Historically impeachment has been the process chosen for removal of Judges, but discussion about Congress' role in defining "good Behavior" and the means for removal have persisted even into the late 1900s. It is entirely feasible that Congress imposes a code of conduct and simple majority review to remove those found in violation. That code of conduct doesn't just have to be about taking free vacations, either. It could assess the quality of judgement and find that if you clearly ignored the facts of a case to push your own narrative (such as with KENNEDY v. BREMERTON) you're in violation.
• Establish a term limit for the Supreme Court and rotate Justices into lower courts when that limit is reached. This one is probably the longest shot as it would depend on whether or not a Justice's "Office" is literally the Supreme Court or the federal Judicial system as a whole and that interpretation would almost definitely be seized by SCOTUS if Congress even attempted this. But, so long as Congress and the Executive are in agreement on the specific interpretation, SCOTUS' opinion here can be suppressed. Worth noting, however, that that is very rarely how the US operates.
• Remove Judicial Review. The idea that the courts have the sole authority to determine the constitutionality of legislation passed by Congress is not found in the Constitution itself, but was manifested by the same court that benefits from granting itself that power. It's the executive branch's job to enforce the law and both Congress and POTUS are elected to represent the people. SCOTUS's job is to resolve conflicts involving the States and those who work with them, they are not accountable to anyone and are not elected. A new law ceding the ability to review constitutionality to some other branch would reset SCOTUS' job to the original intent (a move which I'm sure the 6 textual literalists will gladly embrace).
• Tailor bills to undo recent catastrophic rulings. Congress makes laws. They can make laws that close "loopholes" or perceived ambiguities that SCOTUS uses to derive their rulings. Congress can (and should) undo presidential immunity, Dobbs, judicial review of government agencies' actions, etc.

These will all take work to achieve, and are very unlikely to even be tried, but because they all address shortcomings manifest outside of the Constitution they can all be implemented without amendment to the Constitution.