Bryant,
Yes both of those videos show normal expected behavior. As you have an inverter and that is 60Hz the current to load will go trough zero 120 times a second so what you see on the DC side of the inverter in therms of current will be something like a rectified AC again with current going to almost zero 120 times a second and peak current quite a bit higher than the average current (that 143A the SBMS0 measures).
The fact that there are differences between cells under load means that either contact resistance between cells is a bit different or less likely some cells have higher internal resistance than others.
The ripple is from that 120Hz variation in current that creates the voltage fluctuation and the fact that SBMS sampling rate is not perfectly matching so there is a bit of alias.
What happen with the LCD ? I can send you and LCD if you can solder that.