Jules Verne's fictional character traversed the globe inside 80 days, but McCullum's side have trekked from the depths of despair in January, when they were dismissed for 45 against South Africa, to a state of credibility leading into their final Test match against England on Friday.
The first two Tests have been blighted by poor weather and ended in draws. New Zealand had the better of the first game at University Oval in Dunedin, before Alastair Cook's team took the points at the Basin Reserve in Wellington.
The match at Eden Park starts 79 days after New Zealand's capitulation at Newlands, and given the way the home side has played in patches during the series against England, Verne's novel, "From the Earth to the Moon", may offer a more apt metaphor for their turnaround.
"We were all hurting as much, if not more than the fans and supporters of the team after that South African Test series," McCullum said.
"Since then the way we've responded in short version cricket and in this (Test) series as well, against an outstanding English team, has been really pleasing.
"The thing for us is to remain consistent in our performances and continue to trend in the right direction."
A battling draw and 0-0 finish to the series would be a good result for eighth-ranked Test side New Zealand against the second best team in the world, but swashbuckling strokemaker McCullum said the hosts would press for victory at Eden Park.
"If you look at the history of the way we've played in this series, we're going into this game looking to try and win it," he said.
"There's an opportunity to create history and that's where we'll be turning our attentions to, looking at every situation and how best we can get ourselves in front at the end of the game."
An audacious McCullum told reporters the day before the second Test in Wellington that, should he win the toss at the Basin Reserve, he would ask England to bat first.
True to his word, he sent England's batsmen in, only for Nick Compton and Jonathan Trott to enjoy the placid pitch so much that they both scored centuries and effectively put the home side out of the match by the end of the first day.
McCullum was a little more circumspect on Thursday, saying he would wait until he saw the wicket on Friday before making a decision, but his gut feeling would be to repeat the gambit.
"I still like the option of bowling first. Our philosophy on that hasn't changed," he said with a grin.
"I think if there is anything (out of) the wicket, it will be on day one. Without being 100 per cent committed to that I would still look at the option of bowling first if we have to."
McCullum confirmed they would stick with an attack of three pace bowlers and a spinner, and would have Doug Bracewell available after the paceman successfully negotiated a domestic one-day game for Central Districts on Wednesday.
Bracewell had to withdraw from the first two Tests after cutting his foot on glass but would not be an automatic selection given Neil Wagner's performance in his place, McCullum said.
"We still have to work out what is the best strategy for us. I think the three guys who have bowled for us ... have operated brilliantly throughout the series," he added.
"It has been hard to get the ball out of their hands and the commitment and dedication to the team and efforts they have put in to the last two Test matches, it would be very hard to drop one of them."
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