I find this bike intriguing. But more so after reading clubman's 26 X 1 3/4 rim hypothesis. At second glance, those balloon tires do appear to be much larger than the typical 26 X 1-3/8 tire and there is still a substantial space left between the fender. This would also explain the need for drum brakes as the normal rod brake would not reach the rim. Regarding new tires, a Schwinn S7 balloon tire also has a 571mm bead and might fit. I believe Kenda still makes this tire.
I am looking forward to the after photos and any more information you uncover about this bike.