Sources with direct knowledge tell TMZ ... as the filing deadline approached earlier this week, the group Kanye hired to get his petitions signed -- Let the Voters Decide -- utilized a private jet to make it happen in the nick of time.

We're told the group already had members on the ground in Montana racking up signatures, but due to the state's vast rural landscape ... they needed backup. Fire up the jet.

Our sources say Kanye simultaneously had petitioners working in Utah for next week's deadline there, but to get over the hump in Montana ... a small group was flown over to Big Sky Country to hit up the more populated areas.

Even better for Ye ... the plan worked. We're told the group ended up submitting about 9,000 signatures across multiple counties -- way more than the 5k required -- before Wednesday's deadline.

He's not across the finish line yet though. Candidates file petitions with county officials, who have 7 days to verify signatures before sending a final count to the Secretary of State's Office.

If Kanye still makes the 5,000-count requirement ... he'll be on the presidential ballot as an independent, and be eligible to receive Montana's 3 electoral votes. That's right -- lotta work for 3 votes.

As we've reported ... Kanye is facing opposition to get on the ballot in Wisconsin, and he's been booted from the ballot in his home state of Illinois. The issues in both states are over the validity of the signatures.