Rear wheel drop-out adjustment (1-speed) I've got round to my Twenty/Shopper and besides replacing the tyre also went ahead and got a new KMC chain.
Of course, the links were somewhat shorter, and so I couldn't cut it just right without having to adjust the rear wheel drop-out.
In the end, this is what I got.  

Is this drop-out position safe to ride? The nuts are secured to about 300 inch-pounds  

UPD: I was just reminded KMC sells half-links, so might just get one and a missing link to lengthen the chain a bit. (now I just need to find a K710 missing link somewhere on this continent)
I would not ride that bike, for brake reasons.

1) The rear rim brakes would be out of position.  Hopefully you've re-adjusted the brake pads.  However rim brakes would be safer than other brakes given that dropout.

2) If you have a coaster brake (ie a backpedal brake)  then a hard stop could tear the axle out the front of the dropout, using the ground as a lever-fulcrum.  

3) If you have a drum brake (which is possible given I can see a cable outer and the axle is hollow, perhaps its just not connected in the photos) then the same as for backpedal brakes.

Your safe answer is to simply buy and fit a longer chain.   Yes its annoying.