akima interpolation for irregular grid

Question

I am trying to interpolate a irregular raster grid to a regular grid using akima library in R. However, after I define the regular grid and interpolate the values to the new regular grid, I end up in a strange raster position. I'm doing something wrong but I don't see where. If anyone has a solution (or know a different approach), please let me know. Thank you very much.

library(raster)
library(akima)
library(rgdal)
library(sp)


# download the file
url <- 'https://downloads.psl.noaa.gov/Datasets/NARR/Derived/monolevel/air.2m.mon.ltm.nc' 
file <- paste0(getwd(), "/airtemp.nc")

download.file(url, file, quiet = TRUE, mode = "wb") # less than 4 mb

# define the grid edges according to https://psl.noaa.gov/data/gridded/data.narr.monolevel.html
y <- c(12.2, 14.3, 57.3, 54.5)
x <- c(-133.5,  -65.1, -152.9, -49.4)

xym <- cbind(x, y)
p = Polygon(xym)
ps = Polygons(list(p),1)
sps = SpatialPolygons(list(ps))

# create a spatial grid to 0.3 cell size
xy <- makegrid(sps, cellsize = 0.3)
xy$first <-1
names(xy) <- c('x','y',"first")
coordinates(xy)<-~x+y
gridded(xy)<-T

# read the netcdf file and extract the values
cape <- brick(file)[[1]] #get the first layer only 
rp <- rasterToPoints(cape)
rp <- na.exclude(rp)

# interpolate to the crs for Northern America Conformal Conic
r2 <- project(rp[,1:2], paste('+proj=lcc +lat_1=20 +lat_2=60 +lat_0=40 +lon_0=-96 +x_0=0 +y_0=0 +datum=NAD83 +units=m +no_defs'), inv=TRUE, use_ob_tran=TRUE)

# add the transformed coordinates
rp[,1:2] <-r2
rp <- as.data.frame(rp)

# create a spatial points object and plot it
coordinates(rp)<-~x+y
spplot(rp, scales=list(draw = T))

# interpolate the points to the coordinates (takes a while)
akima.sp <- interpp(x = coordinates(rp)[,1], y = coordinates(rp)[,2], 
                    z = rp@data[,names(rp)[1]],
                    xo = coordinates(xy)[,1],
                    yo = coordinates(xy)[,2],
                    linear = F, extrap = F)

# create a raster file
r.a <- rasterFromXYZ(as.matrix(data.frame(akima.sp)))
plot(r.a)