Transpose a file, and replace missing values by

Please guide with the following data formatting.

I have Readings for Names, from Machines and sometimes these readings are replicated. Where a reading was not found, it is left as blank.

Name Instrument Rep R1 R2 R3 
N1 I1 1 1 2 3 
N2 I1 1 1 3 4
N1 I1 2 2 3 4
N3 I1 2 3 4 5
N1 I2 1 1 2 3 
N2 I2 1 1 3 4
N2 I2 2 2 3 4
N3 I2 1 3 4 5
N1 I3 1 1   4  
N2 I3 1 2 5   
N3 I3 1   6 
N3 I3 2     1

First, I want to consolidate the replicates by using their mean (per name per location). Then, I want to transpose this data and replace the missing values by dot (.) .

What I want in my output is

Reading Instrument N1 N2 N3
R1 I1 1.5 1 3
R2 I1 2.5 3 4
R3 I1 3.5 4 5
R1 I2 1 1.5 3  
R2 I2 2 3 4
R3 I2 3 4 5
R1 I3 1 2 .
R2 I3 . 5 6
R3 I3 4 . 1

Please note that the number of Names and Readings are quite variable, in some files I have 134 readings, some others have 28 etc. but the readings always start from col3.

This is what I tried unsuccessfully for a test run for only one column

awk '
    NR>1{
        arr[$1" "$2" "$3]   += $4
        count[$1" "$2" "$3] += 1
    }
    END{
        for (a in arr) {
            print a, arr[a] / count[a]
        }
    }
' file |  awk '
NR == 1 {
    n = NF
    for (i = 1; i <= NF; i++)
        row[i] = $i
    next
}
{
    if (NF > n)
        n = NF
    for (i = 1; i <= NF; i++)
        row[i] = row[i] " " $i
}
END {
    for (i = 1; i <= n; i++)
        print row[i]
}'