It's a crap job, but someone has to do it ...
OK, the first thing you need to understand is that finding Big Foot(s) requires first of all cutting down that search area and I mean big time.
To do this you need to first of all set up patrols that find and test crap. Yes, I do mean excrement. Their sole function will be to perform a grid search for crap that does not match crap from species they do not know already.
This means collecting lots of crap, noting the GPS coordinates and sending it all in for automated analysis - you're doing this on an industrial scale and you need machines to do the testing.
If Big Foot(s) is(are) out there they have to expel crap sometime. When they do it will come up as an unidentified species. The unidentified ones could just be boring unknown species of something else, but you can do a lot with DNA analysis of those samples and identify which ones are related to known species and have a statistical likelihood of being a Big Foot.
Automated cameras and other search equipment can be used to monitor the entire localized area of interest. These can run 24/7 and computers can analyze images send back. Eventually they'll get a hit.
Now it's carefully trained hunters on the ground who can wait and watch and move in until they get the target.
Just who the hell pays for all this ?
The IRS, meaning the tax payer of course !
Happily these search programs can be funded as part of "normal" wildlife activity. Heck you might even get grants from international agencies to find all those new species they think we're looking for (but don't give a hoot about really). The universities and students will queue up to roam about examining crap, practically for free if you wave some eco-friendly flags at the suckers. We'll lose a few to cougars and bears, but it's not like students are hard to replace by cheap labor, so no problem.
This kind of thing takes time. It's a multi-decade search. But that's the great thing about tax payers - they die and they produce their own replacements, so the money ain't gonna dry up. It's government project so once it's on the books it's virtually impossible to stop and cost over-runs are expected and normal.
Eventually we'll find this Mr. Big Foot and tax that sucker to death. I mean, you knew that was the government's plan all along - grow the tax base.