You're a bit early for most of May and all of June, at least for any awards being released at T-331, AA only allows awards to be booked T-331 days from today which means you can only book through May 14th as is which is why you can't see any space for any dates beyond that.

You ought to be able to find something on a trunk route released at T-331, just be vigilant and check all possible routes for each day as it opens up (aka check for May 15th tmrw, if no luck check for May 16th the next day, etc.)

FWIW, BA is showing J availability for MIA - LIM - EZE on May 14th. I'm new to AA so I don't know the rules entirely but I don't think you'd have any problem tacking on a DCA - MIA to that and going DCA - MIA - LIM - EZE with MIA - LIM - EZE on LAN 767s