Sorry for the slow response, but when in the process of taking out the breakers to investigate the bus bar I figured out what was going on and it took me a few days to confirm it. The two bad breakers were in the same row of my sub panel, and it dawned on me that if one the lines from the main panel that feeds sub panel was bad, that could be causing my problem. So I tested the two breakers (tandem) in the main panel that were feeding my sub and sure enough one of them was putting out 25V. So I replaced the tandem breaker in the main panel and now everything is working agin.
Thank for your suggestion about the breakers being in the same row, which got me thinking about the problem in a different way.
First, everything about the Sonoff stinks like cheap Cheese, so good bet it is not UL listed. RoHS and CE is nothing, and UL/CSA listings are often forged by those offshore manufacturers.
Mains electrical is serious business, and the stuff is already very cheap - $20 for a proper smart switch for instance. The only reason that price seems high is you have found this thing that is cheaper in several ways, most bad. Who cares? There will always be a cheaper piece-o-junk out there. Your time is valuable too.
In NEC jurisdictions you cannot install things not approved by your local inspector, who does not run his own testing lab, but simply gets a list of approved appliances from UL or similar entity. NEC 110.
You cannot mount outside a junction box
An electrical device cannot be mounted outside a junction box as you plan, unless the labeling or instructions tell you to install it that way - the labeling and instructions are part of the UL listing, the listing is contingent on it being installed properly, and it is illegal to install it contrary to those instructions (NEC 110.3).
Parallel switches in your plan are semi-OK
The fact that the Sonoff has netural coming in is simply due to the fact that it is a powered device and needs neutral for its own power. Whether it is switching neutral, I cannot guess: It may be possible to bypass its neutral output and serve the neutral from the other side - that depends (again) on the UL approved labeling and instructions on the device.
If that's the case, then having both the smart switch and the plain switch feed the light should be fine. The key rule is that in any cable, currents must be equal - cancel each other out. That is to avoid eddy-current heating.
Low voltage remote switches are even better
If Deepesh Golani's method of accessing the internal switch works, and (again) is supported by UL approved labeling or instructions, that is an even better way since it does not involve significant currents. If that power is low voltage, you would escape the requirement to use Class 1 wiring techniques, and could run remote switches with thermostat wire for instance.
Best Answer
Sonoff make several different products, if this is their "BASIC WiFi Wireless Smart Switch" it has N,L in and N,L out. It presumably connects L in to L out on receipt of a signal from a remote control.
You show the switches wired in parallel, which should work as you describe:
It is doubtful the device is designed for use inside a ceiling rose. It may be hard to find space there. The device might be unable to dissipate heat in a confined space. Ideally you'd ask the manufacturer for advice.