This is pretty close and changing the names of columns should be within your skillset:
reshape(DF,
varying=c(work= c(3, 7), play= c(4,8), talk= c(5,9), total= c(6,10) ),
direction="long")
EDIT: Adding a version that is almost an exact solution:
reshape(DF, varying=list(work= c(3, 7), play= c(4,8), talk= c(5,9), total= c(6,10) ),
v.names=c("Work", "Play", "Talk", "Total"),
# that was needed after changed 'varying' arg to a list to allow 'times'
direction="long",
times=1:2, # substitutes number for T1 and T2
timevar="times") # to name the time col