Did I understand correctly that the length is the number of marks and not the top mark anymore?

If so, then I basically only had to add two lines to my old MiniZinc solution. I still try optimise the top mark as second criterion.

Code:

include "globals.mzn";

int: n;
int: order; % this is called the length in the new problem.

set of int: LEN = 0..order*order;
array[1..order] of var LEN: marks;
array[1..order*(order-1) div 2] of var LEN: diffs = 
  [marks[j] - marks[i] | i in 1..order, j in i+1..order];

% Old Golomb constraints.
constraint increasing(marks) /\ marks[1] = 0 /\ alldifferent(diffs);
% Break symmetry (optimisation): First difference is smaller than last one.
constraint diffs[1] < diffs[order*(order-1) div 2];
% Extra constraint: diffs 1..n appear.
constraint global_cardinality(diffs, 1..n, [1 | i in 1..n]);

solve :: int_search(marks, input_order, indomain_min, complete) minimize marks[order];
output ["\(show_int(-3, order)) \(show_int(-3, marks[order]))"] ++ [" \(x)" | x in marks] ++ ["\n"];

Challenge output:

Yes to first challenge.
n = 14: 7   26  0 1 7 9 12 22 26
n = 15: 7   26  0 1 7 9 12 22 26

Yes to second challenge (there is even a length 7 ruler):
n = 16: 7   31  0 4 6 9 16 17 31
n = 17: 7   31  0 5 7 13 16 17 31

Shortest rulers:
n =  1: 2   1   0 1
n =  2: 3   3   0 1 3
n =  3: 3   3   0 1 3
n =  4: 4   6   0 1 4 6
n =  5: 4   6   0 1 4 6
n =  6: 5   11  0 1 4 9 11
n =  7: 5   11  0 2 7 8 11
n =  8: 5   11  0 2 7 8 11
n =  9: 5   11  0 2 7 8 11
n = 10: 6   17  0 1 4 10 12 17
n = 11: 6   17  0 1 4 10 12 17
n = 12: 6   17  0 1 4 10 12 17
n = 13: 6   17  0 1 4 10 12 17
n = 14: 7   26  0 1 7 9 12 22 26
n = 15: 7   26  0 1 7 9 12 22 26
n = 16: 7   31  0 4 6 9 16 17 31
n = 17: 7   31  0 5 7 13 16 17 31
n = 18: 7   31  0 5 7 13 16 17 31
n = 19: 8   35  0 4 5 17 19 25 28 35
n = 20: 8   35  0 4 5 17 19 25 28 35

The length is slightly worse than suggest by the trivial lower 
bound from (length choose 2) >= n, e.g. length = 6 for n = 10 
but 5 choose 2 = 10.