Not sure if the naïve approach is "Good Enough", but here it is for reference. I sort the list; pack one item into each bin (of 31); then reverse the bins for the next pass, thus hoping to balance out the weight.

Results:

Bin 1 (946): 311 151 151 124 123 86
Bin 2 (933): 296 152 150 124 123 88
Bin 3 (898): 261 152 150 124 122 89
Bin 4 (897): 257 153 150 124 122 91
Bin 5 (859): 216 154 149 126 122 92
Bin 6 (855): 210 154 148 126 122 95
Bin 7 (848): 203 154 147 126 122 96
Bin 8 (846): 199 155 147 126 122 97
Bin 9 (845): 198 156 146 126 121 98
Bin 10 (845): 198 156 145 127 121 98
Bin 11 (847): 197 157 145 128 121 99
Bin 12 (846): 196 157 144 129 121 99
Bin 13 (844): 195 157 144 129 120 99
Bin 14 (845): 195 158 144 129 120 99
Bin 15 (845): 193 158 143 130 118 103
Bin 16 (846): 192 160 143 130 118 103
Bin 17 (842): 188 160 143 130 118 103
Bin 18 (840): 187 160 142 131 117 103
Bin 19 (837): 183 160 141 131 117 105
Bin 20 (836): 182 161 141 131 116 105
Bin 21 (837): 182 161 141 132 116 105
Bin 22 (837): 181 162 141 132 116 105
Bin 23 (836): 180 162 140 132 115 107
Bin 24 (836): 177 163 139 133 115 109
Bin 25 (837): 177 164 139 133 115 109
Bin 26 (840): 177 165 139 134 114 111
Bin 27 (837): 174 166 138 134 114 111
Bin 28 (836): 173 166 137 135 114 111
Bin 29 (837): 173 167 137 135 113 112
Bin 30 (835): 172 167 136 135 113 112
Bin 31 (835): 171 168 136 135 113 112
[download]

And the code:

#!/usr/bin/perl
use strict; use warnings; use 5.010;
use POSIX 'ceil';
use List::Util 'sum';

my @a = sort { $b <=> $a } qw(
  121 182 111 160 105 113 121 97 123 157 133 161 141 135 137 145 133 1
+37
  151 118 126 141 174 181 154 109 198 114 122 162 91 99 116 122 195 19
+9 150
  192 163 88 112 157 182 210 124 105 144 166 144 257 164 156 173 154 1
+93
  142 143 126 118 130 107 86 131 154 131 147 134 118 115 135 141 158 1
+29
  143 126 128 134 129 167 130 135 117 127 146 96 117 99 99 139 152 149
+ 136
  105 124 136 160 160 139 177 115 123 103 150 183 132 171 121 114 111 
+113
  131 144 122 141 111 139 145 109 114 122 103 160 153 147 172 155 122 
+296
  124 112 161 124 311 99 157 122 120 198 152 140 162 177 98 138 156 17
+7 103
  180 187 173 150 135 168 132 196 112 195 126 113 116 105 116 151 216 
+188
  158 121 166 148 132 89 197 92 115 98 130 103 120 261 143 126 167 203
+ 95
  165 129
);

my $bins = pack_n( ceil(@a/6), \@a );
show_bins( $bins );


sub pack_n {
  my ($n, $data) = @_;
  my @bins;

  my $i = 0;
  my $delta = 1;
  for (@$data) {
    push @{$bins[$i]}, $_;
    $i += $delta;

    if ($i >= $n) {
      $i = $#bins;
      $delta = -1;
    } elsif ($i < 0) {
      $i = 0;
      $delta = 1;
    }
  }
  return \@bins;
}


sub show_bins {
  my $bins = shift;
  my $i = 1;
  for (@$bins) {
    my $size = sum @$_;
    say "Bin $i ($size): @$_";
    $i++;
  }
}
[download]