Read multiple xlsx files with multiple sheets into one R data frame

I have been reading up on how to read and combine multiple xlsx files into one R data frame and have come across some very good suggestions like, How to read multiple xlsx file in R using loop with specific rows and columns, but non fits my data set so far.

I would like R to read in multiple xlsx files with that have multiple sheets. All sheets and files have the same columns but not the same length and NA's should be excluded. I want to skip the first 3 rows and only take in columns 1:6, 8:10, 12:17, 19.

So far I tried:

file.list <- list.files(recursive=T,pattern='*.xlsx')

dat = lapply(file.list, function(i){
    x = read.xlsx(i, sheetIndex=1, sheetName=NULL, startRow=4,
              endRow=NULL, as.data.frame=TRUE, header=F)
# Column select 
    x = x[, c(1:6,8:10,12:17,19)]
# Create column with file name  
    x$file = i
# Return data
    x
  })

  dat = do.call("rbind.data.frame", dat)

But this only takes all the first sheet of every file

Does anyone know how to get all the sheets and files together in one R data frame?

Also, what packages would you recommend for large sets of data? So far I tried readxl and XLConnect.