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You might also consider the Yale School of Forestry and Environmental Studies. I have no idea how hard it is to get in there (surely it requires less math than the straight Econ PhD), but I do know that Forestry students are allowed to take Econ PhD classes if that's what they want to do.
Will you be able to handle these courses without real analysis? I think the answer is yes-- if you would have been able to handle them with real analysis. People on this board emphasize the importance of RA as an admissions signal, and they're probably right, but I'm not sure you actually need much RA once you arrive at a program, at least not for the core courses. I just finished my first year (passed comps!), and it was quite hard. But almost none of that difficulty was attributable to challenging concepts from RA. In fact, if you can do the rest of the stuff, it should be pretty easy to pick up the limited RA you need as you go along.
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