Although these thoughts essentially point in different directions as to your question, I think they are both worth considering.
First, I agree there is nothing wrong with choosing a favorite LAC over any research university, no matter how big a name that university has, if you think you are more likely to thrive at an LAC. Obviously that is very personal and different people will go different ways on this question. But I just think between the importance of those four years for their own sake, and then the importance of actually doing really well in college, all that trumps any sort of general fame considerations.
Of course convincing relatives, peers, and so on that it is OK to turn down a more famous university can sometimes be a challenge. But it is your life, and at least it can be worth fighting for what you really want.
Second, I am very skeptical that applying ED2 will actually help many, if any, high need Internationals. There is a lot behind that skepticism, but the bottom line is a college only plausibly has an incentive to “boost” an ED applicant if it thinks you would otherwise be very likely to choose a different offer RD. This is basically why Harvard, Yale, Princeton, Stanford, and MIT don’t even offer ED–they know you are reasonably likely to accept their offer no matter what.
And as a high need International, it is pretty unlikely you will be getting a long great offers (barring something extraordinary). In that sense, for you, every college is HYPSM, meaning I really doubt they are going to be overly worried about losing you if they admit you RD. It is more just a matter if they want you bad enough to spend some of their very limited International aid budget on you, rather than someone else.
Of course one might ask if this applies to need blind colleges like Bowdoin, and I suspect yes. Basically, because they are need blind and meets need, something like 2/3rds of their Internationals end up being on very large aid packages. And then their overall International acceptance rate is like 1.9%, versus 11.4% for domestic applicants. Again, all this fits with the idea that Bowdoin might was well be HYPSM for a high need International.
OK, so if you want to apply ED2 to Bowdoin because Bowdoin is your remaining favorite, then I think that is fine because Bowdoin could rationally be your favorite. If you don’t want to apply ED2 to Bowdoin because you want to see what offers you get before deciding, then I think that is also fine because I am skeptical applying ED2 to Bowdoin would change what Bowdoin is going to do anyway.