She's a beauty. Excellent photos, as well.
That is most definitely a "presentable post"!

The M1905, I believe, was indeed manufactured in smaller numbers than the M1908 or M1910 and far fewer than the M1903.

That high gloss finish may be original. My cased M1910 Takedown, also Vienna proofed 1922 along with British proofs, has that finish. I know it's unchanged from 1932 when my grandfather purchased it 'second hand' in Ceylon. It, too, has the grip cap storage (with spare sight bead therein) as well as the optional folding peep sight.

This is not my MS, it's a photo swiped from the 'net.

Your cleaning rods appear absolutely proper for the MS (I just brought mine out to compare) but are you missing one? They did come in four or five piece versions. Mine has five segments measuring 6.9 inches each. The brass 'jag' end looks just like yours. Do your other three segments all have both ends threaded?

Of my five steel segments, one has the brass 'jag' at one end (not threaded) with the other female threaded as yours in the image, three have a male threaded steel end and brass slotted, female threaded other end (as three in your image), then a fifth one with one end male threaded and the other shaped and slotted like the brass ends but all steel with no female thread - it is smooth at the end.

Mine does have a 60cm barrel, but it seems a four piece rod set would have two segments with both ends threaded, one with only female and one with only male threads so they assemble with smooth ends.

Here is your Lyman 1A, a nice bit of kit: