I was playing with my HDG2002B a bit in the last week.
It seems we might be stuck with Hantek old crappy u-boot and kernel for now. S3C2416 is an old platform that is not actively maintained by the OS community.
From what I've seen in current mainline u-boot s3c24xx is supported in general, but booting doesn't seem to work. s3c24xx has a special boot process where it loads and executes first 4kB from flash for the early stage bootloader and this bootloader has to load the rest. In u-boot case this is called "SPL", but this part doesn't cover s3c24xx.
Embedsky wrote these routines (loading rest of the u-boot from flash) by hand in their old u-boot (2009, the one Hantek uses).
With linux kernel situation is similar, but slightly better.
Nowadays the way to configure linux kernel for a particular board is to use Device Trees. Before each board designer added a bunch of source and header files for each and every possible arm board and Linus got mad merging this mess.
So now there are little scripts called Flattened Device Trees that are compiled into binary form and kernel parses them on boot and loads and configures peripherals appropriately.
Again, s3c24xx is poorly maintained and while many s3c peripheral drivers migrated to new device tree configuration (interrupt controller, pin controller, pwm, uarts, spi, i2c, hs-mmc, dm9000) there are few crucial things that need the old approach (framebuffer, nand, dma engine).
Other than that linux-4.x seems to boot fine over tftp/NFS on the HDG2002B. For now I'm trying to limit the number of kernel warnings/errors and get all peripherals properly detected (figuring out GPIO pins and EINT lines). Later I'll test them in practice one by one.
Current boot log:
http://pastebin.com/Tf3cKspW