R - Speeding up loop over array dimensions

I am working with an array with dimensions

[1] 290 259  55   4

For each repetition of the last three dimensions, I want to perform a rolling mean on the 290 elements of the first dimension, reducing the number of elements to 289. Finally, I need to create a data frame with the updated values.

The following code achieves what I need, but it takes a LONG time to run (actually, I have to interrupt it before the end).

library(zoo)

# Generate random data with same dimensions as mine
my.array <- array(1:16524200, dim=c(290,259,55,4))

# Get dimension sizes
dim2 <- dim(my.array)[2]
dim3 <- dim(my.array)[3]
dim4 <- dim(my.array)[4]

# Pre-allocate data frame to be used within the loop
df2 <- data.frame()

# Loop over dimensions
for (i in 1:dim4) {
  for (j in 1:dim3) {
    for (k in 1:dim2) {

      # Take rolling average
      u <- rollapply(my.array[,k,j,i], 2, mean)

      # Assemble data frame
      df1 <- data.frame(time=i, level=j, lat=k, wind=u)
      df2 <- rbind(df2, df1)

    }
  }
}
# Very slow, and uses only one machine core

I feel like it is possible to improve the processing time of this code by using vectorization or even some kind of parallelism, but I can't figure out how.

Any suggestions to make this code more efficient?