Ross Perot in 1992 collected more signatures than any presidential candidate in history. He used the independent petition method in every state except in Oregon, even though the signature burden on him would have been lighter if he had formed new one-state parties in certain states. Also he did not accept the nomination of any pre-existing ballot-qualified party in 1992. Also, back in 1992, the ballot access laws for presidential candidates running outside the major parties were more severe than they are today.
On July 31, the Robert F. Kennedy, Jr. held a press conference about ballot access, and asserted that he had collected over 1,000,000 signatures, a record. The claim that this is a record is not true, because of the Perot example. It is also that Lenora Fulani in 1988, John Anderson in 1980, and George Wallace in 1968 collected more than 1,000,000.
See this statement from the Kennedy campaign. Kennedy did not need to collect any signatures in California or Florida, because ballot-qualified parties that themselves didn’t need any signatures nominated him. Also he needed fewer signatures than Ross Perot needed in 1992, because of easier requirements now than in 1992, in Connecticut, Georgia, Hawaii, Maryland, Michigan, Missouri, Montana, North Carolina, Oklahoma, Oregon, Pennsylvania, Virginia, and Wyoming.