Reshaping an array to data.frame

df = melt(x) gives you something very similar to what you want. Then you could compute the various measure variables from the different levels of measure.

Using the "reshape2" package, try:

dcast(melt(x), Subject + Cond + Item ~ Var4)

Yes, use adply():

adply(x, c(1,2,3))
   Subject Cond Item Measure1 Measure2 Measure3
1       s1    A    1    -0.93   -0.360   -0.005
2       s2    A    1     0.39    1.043    1.090
3       s3    A    1     0.88    0.330    0.360
4       s4    A    1     0.63   -0.120    0.040
5       s5    A    1     0.86   -0.055    0.090
6       s1    B    1    -0.69    0.070    0.170
7       s2    B    1     1.02    0.670    0.680
8       s3    B    1     0.29    0.480    0.510
9       s4    B    1     0.94    0.002    0.090
10      s5    B    1     0.93    0.008    0.120
11      s1    A    2    -0.01   -0.190   -0.050
12      s2    A    2     0.79   -1.390    0.110
13      s3    A    2     0.32    0.980    0.990
14      s4    A    2     0.14    0.430    0.620
15      s5    A    2     0.13   -0.020    0.130
16      s1    B    2    -0.07   -0.150    0.060
17      s2    B    2    -0.63   -0.080    0.270
18      s3    B    2     0.26    0.740    0.740
19      s4    B    2     0.07    0.960    0.960
20      s5    B    2     0.87    0.440    0.450

Use as.data.frame.table().

d0 <- as.data.frame.table(x)
head(d0)

#   Subject Cond Item     Var4  Freq
# 1      s1    A    1 Measure1 -0.93
# 2      s2    A    1 Measure1  0.39
# 3      s3    A    1 Measure1  0.88
# 4      s4    A    1 Measure1  0.63
# 5      s5    A    1 Measure1  0.86
# 6      s1    B    1 Measure1 -0.69

library(tidyr)
d1 <- pivot_wider(data = d0, names_from = "Var4", values_from = "Freq")
head(d1)

#   Subject Cond Item Measure1 Measure2 Measure3
# 1      s1    A    1    -0.93   -0.360   -0.005
# 2      s1    A    2    -0.01   -0.190   -0.050
# 3      s1    B    1    -0.69    0.070    0.170
# 4      s1    B    2    -0.07   -0.150    0.060
# 5      s2    A    1     0.39    1.043    1.090
# 6      s2    A    2     0.79   -1.390    0.110