This will be a tough one, for several reasons.
As seen on the pictures, the main controller (SoC) is an OMAP-L138 E ZWT from Texas Instruments.
Dual Core SoC: ARM926EJ-S (ARM9 RISC CPU) + C674x (DSP CPU) + loads of peripherals
E = Silicon Revision 2.3 (latest)
ZWT = 361-Pin Plastic BGA, with Pb-free Soldered Balls, 0.8-mm Ball Pitch, 16,00 mm x 16,00 mm
I've done a longer search in your dump. Here's what I found so far:
TIPA YSX - Texas Instruments Application Image Script, generated by AISgen tool
UBIFS - Unsorted Block Image File System
JFFS2 - Journalling Flash File System v2
U-Boot 2010.12 (Oct 19 2018 - 15:50:09)
QNX4 (this should be the OS, although I found mentions of different Windows versions)
Linux-2.6.32-rc6 - kernel version
I wasn't able to extract anything useful from the image, besides some random garbage and PNG files. There are at least 12 GZIP compressed streams inside, but all are mangled, so not possible to extract. This could be because of the way the UBI file system writes to the flash and scattering/distributing/fragmenting the data. I've tried really hard, without success. Also I could not identify the beginning of any file system yet, although I see 3708 + 531 UBI FS blocks. Need to dive into that FS some more...
Now, first thing to do would be to locate the UART port, then we can observe the boot process, AND, if we are lucky, are presented with some boot options (try hitting SPACE or ESC key during boot).
There's a RS232 connector on the digital board:
XP8 on R30_0K's - board revision 2.2 (2018-09-10)
XP3 on alpher's - board revision 1.0 (2017-06-28)
XP3? on shortfoxyman's - board revision 1.0 (2017-06-28) - no bottom pic provided
If you don't know the pinout, check which pin is GND, the other one would be data. Connect them to your scope, one pin on each channel. Turn on the device and watch for the data bursts. This one is the TXD line, the other one RXD. Note the amplitude of the signal, it goes up to +/-15V. You will need a RS232<->USB adapter, then connect TXD of the device to your RXD input and vice versa. Set your serial COM port to 115200 8N1. Not sure, but maybe the USB port provided there could be a virtual COM port already, so you might want to connect a USB cable there and see what comes up in your device manager in Windows.
You might also want to try via web browser:
192.168.1.9 / 255.255.255.0
or
192.168.2.5 / 255.255.255.0
There could also be a TFTP server running, standard port is 69 UDP. Try a READ request, using any random TFTP client. You could do a port scan as well to find other running services like FTP (21), SSH (22) or Telnet (23).
Plenty of things can be tried.
Side notes:
1) I don't own one of these myself (yet!)
2) I am not familiar with TI devices (is anyone here?)
It MIGHT not even be a firmware problem. As OWON previously replaced whole boards without requesting them back for repair, this could also indicate cold (F)BGA solder joints, for instance. The effort of repair would be too high in this case, but a FLASH rewrite should be easily doable for a manufacturer. They know their own programming ports and know how to access them. This should be a matter of 10-20min per unit, worth repairing actually.
Anyway, I'm curious how far we can get. With the combined, unparalleled power of our global experts on here

GANBATTE NE!