Sorry.My assistants have left a short while ago and so it is difficult for me to upload a diagram.
My suggestion is you please take a mirror image of your diagram,merge the 'B' lines into one and designate it as 'N' (i.e neutral).The 'A' designates phase wire from 120V source. Now you have got a pseudo MWBC.You can easily see the neutral will be overloaded in this circuit.......
If the supply is a two lead source technically there is no neutral.
If the supply is a 3 lead 120/240m source and you are only using one lead plus neutral you still have same thing at this panel for all practical purposes of this discussion.
If this panel is supplied by a feeder there is no way to overload anything if proper ovefrcurrent protection is applied to the feeder.
If this panel is supplied by a service (which the OP says "non-service rated panel" so that would be a problem right there) you would need the grounded conductor to have the sum of the ampacity of the two ungrounded conductor ampacities to prevent overloading.
Have done this many times on farms where supplying some outbuilding with 120 volt only and limited loads like two circuits only.
Lets say we only have two 20 amp circuits - the grounded conductor needs to be at least 40 amps, the ungrounded conductors can be only 20 amps if running two of them otherwise 40 amps if running a single conductor.
If you are supplying a 100 amp panel with two 100 amp capacity ungrounded conductors you will need a 200 amp grounded conductor, in most cases you should also seriously consider making this 120/240 if there is any way possible.
Most of the time when this is done it is in places where the load is somewat minimal.