Former Labour Party leader David Shearer was the most recent to be questioned after Kim Dotcom named him as the MP he liked most on TVNZ's Q+A programme. Alas, it seemed Dotcom had flung his name out as a decoy duck.
Shearer was blissfully oblivious to his favoured son status because he was otherwise occupied on his boys' trip to Beijing in the company of yet another former leader of the Labour Party, Phil Goff, and the calming influence of NZ First leader Winston Peters.
Which brings us to the second Bigfoot hunt of the season - Peters' search for a successor.
In this quest, it is Shane Jones who has been the most rigorously pursued, not least because of a long and very obvious trail of scat right under the noses of the trackers.
Suspicion began when Jones was observed spending a lot of time with his buddy from the north, including consulting with Peters over his planned attack on the supermarkets under Parliamentary privilege. It grew when he admitted his chances of leading the Labour Party had gone even before they arrived.
It grew further when, days after being publicly ticked off by his boss for baiting the Greens, he reprised the squawking mollyhawk theme by saying their reaction to a major report on climate change amounted to "pushing the shrill button".
Despite all this, Jones claimed it was all a false trail that would lead the hunters to nothing more than a wild goose.
Jones' leader, David Cunliffe, meanwhile continued his hunt for popularity but had a setback with two further polls showing his rifle was still backfiring.
Finance Minister Bill English also got in on the action with his ongoing hunt for a surplus.
There is just a month to go until he is expected to serve his fatted surplus up on a plate with all the trimmings in the Budget.
Key put in a progress report in a pre-Budget address yesterday, observing the surplus was firmly in the crosshairs, but adding it would be very lean meat indeed and the trimmings would be sparse, the gravy little more than a watery drizzle.
He took the Weight Watchers approach to his sales pitch. He assured voters too much fat was bad for them and sweeties were even worse, thereby putting paid to any hopes of the kind of hunt that can be enjoyed by all - the lolly scramble.
He told the voters to be wary of Greeks bearing gifts - in this case Labour with its Trojan horse stacked with promises of cheap housing and money for all babies.
He conveniently forgot that when National was trying to win the election in 2008, it had been in the same position with its horse full of tax cuts, and that had worked a treat.
The Green Party produced the results of its own vegetarian-friendly hunt this week: for a sense of humour.
Green MPs are renowned for their earnestness, especially in the modern day as they try to project an image of a more business-like, professional force.
This apparently requires an inability to indulge in frivolity. It showed only last week, when MP Gareth Hughes decided to join a Twitter game of coming up with a variation on a children's book title that ruined the book. Not one to miss a chance to make a political point, Hughes' contribution was "GE Eggs and Ham".
Nonetheless, the Greens managed to knock together their collective funnybones to come up with the annual April Fool's news release - the one time of year they take the mickey out of themselves. This time round it was the declaration that the Greens would replace the Crown limos with horses.
Like all good April Fool's jokes, some bits were so believable they could have been mistaken for the truth. So it informed us some MPs were testing other forms of travel, including Catherine Delahunty "doing her bit by astral projecting to Wellington".
Finally, spare a thought for Independent MP Brendan Horan, a solitary figure galloping over the moors on the hunt for the most elusive creature of all: relevance.
