Thanks to guidance from Benoit Simon-Bouhet, I see that by setting the
projectRaster flag over to TRUE
aleu.r.geo<-marmap::as.raster(aleu, over=TRUE)
and using a projection with the longitude of origin set to be 190; I get
the desired raster that extends across the antimeridian even when projected
to the azimuthal equidistant projection.
prj.StudyArea <- CRS("+proj=aeqd +lat_0=55 +lon_0=*190"*)
#Azimuthal Equidistant -170, 55