Yes we start if by researching the Hinago Medical Facility. At the same time we have the Pangolins apply a little lead pipe interrogation to the Condor resistance to find out where the summoner has gone.
So...the Hinago Medical Facility
might generate a lead. I say "might" because it is physically possible for a lead to be generated. And I use this language because my personal opinion is that the Hinago Medical Facility will
not end up generating such a lead.
The Condor Resistance giving up the Summoner's location...is possible. More important is her identity, obviously. Why? Because we already have knowledge that the Condor Summoner is either a Mist-nin in good standing with Mist or a Mist-aligned ninja in good standing with their village. Which leads me to a related issue.
I don't see how we can get the Condor Summoning scroll (and, more importantly, use it) without
killing the previous owner. Which is a problem because said user is either a Mist-nin in good standing with Mist or a Mist-aligned ninja in good standing with their village. The Chūnin Exams are a time where all the villages say "we aren't fighting each other, doing otherwise is an act of war". Us going off to kill a foreign ninja in good standing with their village breaks that agreement, and now everyone is bulldozing Leaf. Because of us. And if your response is "Well, we don't have to show that we got the scroll until later...", then I counter-ask "Why are we doing this
now instead of after the ceasefire?".
The Capybara Summoning Scroll may or may not have the kill-a-village-nin issue (I don't know if it's been signed since the aborted meeting) but comes with the even greater issue of "we have even fewer leads".
As for why we go instead of is for 2 facts. First we have shown our ability in the current event to destroy chunnin level opposition. Second because we are going to get a solid plan together that we will pitch to Jiraiya. If he then points out the dangers we suggest that a jounin leader could be assigned. We then suggest Kakashi as an option
This...doesn't really answer the question I asked. All it shows is that a) we can demolish low-mid tier opposition, which isn't necessary if
Hatake Fucking Kakashi is getting involved, and b) we made the plan, which...makes us necessary why, exactly?
And the above issue regarding killing a foreign ninja in good standing with their village. And the extremely low probability we'd be able to find two Summoning Scrolls within a single month, even with Kakashi's assistance, as stated above. And the fact that we can't efficiently train/research while on the road. And the literal inability of us to get involved in politics/social (which admittedly isn't such a bad thing).