wide to long multiple measures each time

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

The most concise way is to use tidyr combined with dplyr library.

library(tidyr)
library(dplyr)
result <- DF %>%
  # transfer to 'long' format
  gather(loc, value, work.T1:total.T2) %>%
  # separate the column into location and time
  separate(loc, into = c('loc', 'time'), '\\.') %>%
  # transfer to 'short' format
  spread(loc, value) %>%
  mutate(time = as.numeric(substr(time, 2, 2))) %>%
  arrange(time)

tidyr is designed specifically to make data tidy.

Oddly enough I don't seem to get the same numbers as you (which I should since we both used set.seed(10)?) but otherwise this seems to do the trick:

library(reshape)  #this might work with reshape2 as well, I haven't tried ...
DF2 <- melt(DF,id.vars=1:2)
## split 'activity.time' label into two separate variables
DF3 <- cbind(DF2,
             colsplit(as.character(DF2$variable),"\\.",
                      names=c("activity","time")))
## rename time, reorder factors:
DF4 <- transform(DF3,
                 time=as.numeric(gsub("^T","",time)),
                 activity=factor(activity,
                   levels=c("work","play","talk","total")),
                 id=factor(id,levels=paste("x1",1:10,sep=".")))
## reshape back to wide
DF5 <- cast(subset(DF4,select=-variable),id+trt+time~activity)
## reorder
DF6 <- with(DF5,DF5[order(time,id),])

It's more complicated than @DWin's answer but maybe (?) more general.