I would be surprised if this MCU doesn't support an ISP mode, but it's not impossible.
For personal interest, I will look it up. And avoid this MCU if it is the case ... ;-O
I overlooked that you mentioned "custom board". Which probably means there is no support designed in.
> Additionally, this MCU doesn't have the UART interface. It's a minimalistic MCU.
UART is just the most common. Many system ROM bootloaders support other interfaces like SPI, CAN, or even USB.
But as said, I will check the DS / user manual, and see if I can find something.
Deep sleep modes are known to break debug access.
I suppose it would help to add a wake-up source than can be manually operated, like a GPIO level transition.