Your PO was an "interesting character." I didn't understand before that those glorified clotheslines ARE the lower shrouds. Suspected, but wasn't sure. I'd definitely get them off, post-haste.
PO was trying to set up running back stays, hence the useless snap shackles and the two deck eyes. Upwind, he snapped his shrouds to the fore deck eye, downwind he snapped the windward shroud to the aft deck eye and left the leeward stay at the front deck eye (to clear the boom).Jibing must have been great fun, either a truly hair-raising experience or very slow, Hudson-River style. Anyway, this is all totally unnecessary, 1000's of DSes and other dinghies sail perfectly well upwind and down without backstays! The "secret" is the swept spreaders, as long as the chain plates are abaft the mast and everything is properly tensioned, you have enough fore-aft stability to go downwind. The spreaders "push" the mast forwards, the forestay keeps it from going backwards, all is well. Which brings us to the clotheslines that PO used, there's no way to tension that enough for any real effect on the mast (more than you already have from the wire shrouds). Even if you were able to tension them somehow (most real running back stay rigs use a purchase) and overcome the stretchiness, you'd then either destroy those snapskackles or pull those ridiculously thin eyestraps out of the mast. Also the eyes should be riveted, not screwed to the mast, but at this point it hardly matters.
Previous paragraph just to explain why I write "take those things off now." I'd also like to point out that previous owners didn't necessarily know what they were doing, bless their salty hearts. Remember, the DS was built and sold as the "Volkswagen Bug of the Sea." OK, that wasn't the slogan, but you get the point - Everyman's Sailboat. But not every man (or woman) knows how to properly rig a boat....
Hmm, I just realized that for my Daysailer:Volkswagen analogy to work, Uffa Fox would be Ferdinand Porsche (certainly apropos) and George O'Day would be... Nevermind!
See you on the water!
Tom
PS, betcha the padeyes under the rub rail were for fenders... Your PO really liked belt-and-suspenders solutions!