How can I convert the duration so it appears as the number of days?
As an other solution we could utilize difftime, e. g.:
unitnames = c(week="weeks", weeks="weeks", day="days", days="days", hour="hours", hours="hours",
              minute="mins", minutes="mins", second="secs", seconds="secs")
converdays =
function(w)
{ sapply(strsplit(w, ", "),  # for each string, separate the quantities by ", "
         function(x)
           do.call(sum,      # sum up the duration quantities, computed such:
                   lapply(strsplit(x, " "),  # split into magnitude and unit
                          function(y)        # convert to a "difftime" with that unit
                          { z = as.difftime(as.integer(y[1]), units=unitnames[y[2]])
                            units(z)="days"  # change that unit to the desired "days"
                            return(z)
                          }
                         )
                  )
        )
}
converdays(Duration_1)
# [1] 3.027911e+02 1.388889e-04 2.358796e-02 7.920139e-02 3.824074e-02
converdays(Duration_2)
# [1] 6.365741e-04 8.865741e-01 2.032581e+00 5.785648e-01 1.112341e+02
Another variant, should one prefer the output to keep the class difftime in order to be able to easily convert to different units, is:
unitnames = c(week ="weeks", day ="days", hour ="hours", minute ="mins", second ="secs",
              weeks="weeks", days="days", hours="hours", minutes="mins", seconds="secs")
csplit = function(x, s, f) do.call(c, lapply(strsplit(x, s), f))  # helper function to split
convertds = function(w)                  # convert to difftimes
             csplit(w, ", ",             # for each string, separate the quantities by ", "
                    function(x)
                     sum(csplit(x, " ",  # split into magnitude and unit, convert and sum up
                         function(y) as.difftime(as.integer(y[1]), units=unitnames[y[2]]))))
print (convertds(Duration_1) -> d1)
# Time differences in secs
# [1] 26161153       12     2038     6843     3304
units(d1)="days"
d1
# Time differences in days
# [1] 3.027911e+02 1.388889e-04 2.358796e-02 7.920139e-02 3.824074e-02