I don't have a source for this, but I am pretty sure that it is locked to always being Male, unfortunately.Is the HA Eevee available ingame male-locked? The guides and community seem to have differing opinions on this with some claiming it male-locked and some saying female is available (bulbapedia shows the female icon). Has anyone ever got a female Eevee?
As for the Gym Leaders in Join Avenue, my experiences are mostly the same as those of Aquarelle. The Gym Leaders seem to appear very often once you get to higher levels, I usually got at least one every day when my Avenues were at high levels. Again, this is nothing that is confirmed but it seems to be the clear case if anything.