Issues adding properties to multigraph

Question

Bug persisting through 12.0

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Unsupported Functionality (loosely, a bug)

Mathematica (as of 11.0.1 for Mac OS X x86 (64-bit) (September 21, 2016)) does not support multi-graph where edge properties vary between two nodes that share multiple edges. Although this is not recognised officially by Wolfram with a bug reference number they could provide, it is a failure to fully provide multi-graph support.

While the following yields False the feature remains unsupported:

g1 = Graph[{1, 2, 3, 4, 5}, {1 <-> 2, 1 <-> 2, 2 <-> 3, 4 <-> 4, 
    5 <-> 1, 2 <-> 4},
   EdgeWeight -> Range[6]];
PropertyValue[{g1, #}, EdgeWeight] & /@ EdgeList[g1] == Range[6]
(*FALSE*)

Original Issue

Today I was working with a large multi-graph with properties on the edges when I discovered that properties aren't assigned as expected.

My preferred graph construction method is to specify properties before creating a graph, using the following undocumented syntax:

Graph[{vertices},{edges)]

The following minimal example shows my problem, the two edges 1<->2 have been given different values of the Property "foo" - but that's not what PropertyValue reports:

seGraph1 = 
 Graph[{1, 2, 3, 4}, {Property[1 <-> 2, "foo" -> 1], 
   Property[1 <-> 2, "foo" -> 3], Property[2 <-> 3, "foo" -> 5], 
   Property[3 <-> 4, "foo" -> 6]}]
seGraph2 = 
 Graph[{1, 2, 3, 4}, {Property[1 <-> 2, "foo" -> 30], 
   Property[1 <-> 2, "foo" -> 10], Property[2 <-> 3, "foo" -> 5], 
   Property[3 <-> 4, "foo" -> 6]}];
PropertyValue[{seGraph1, #}, "foo"] & /@ EdgeList[seGraph1]
PropertyValue[{seGraph2, #}, "foo"] & /@ EdgeList[seGraph2]
(*{3,3,5,6}*)
(*10,10,5,6}*)

Not one to stick to undocumented naughtiness, I also tried adding properties after the creation of the Graph. But the same problem:

seGraph3 = Graph[{1 <-> 2, 1 <-> 2, 2 <-> 3, 3 <-> 4}];
MapThread[(PropertyValue[{seGraph3, #1}, "foo"] = #2) &, {EdgeList[
    seGraph3], {1, 3, 5, 6}}];
PropertyValue[{seGraph3, #}, "foo"] & /@ EdgeList[seGraph3]
(*{3, 3, 5, 6}*)

Question

Is there a way to build a multigraph with different PropertyValues for identical edges?

Note: I'm on 10.1 for at least a few more days, but I'd happily have a solution that will work for 10.2