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Checkout http://pdp10.nocrew.org/docs/instruction-set/pdp-10.html for detailed info on the PDP-10 instruction set

Get the Panda Tops-20 distribution for the Ka10.

Then find either an assembler or use the debugger.

The final KL10B permitted up to 32 256K word sections.

I am curious, do you know if user-mode programs had access to more than a single 256K word address space? Did they add something like segment registers or a split between Data and Instruction space?

The answer is yes they did. I think the PC was extended and you switched explicitly between segments via a small set of instructions, so code/data can't span segments. I think of it as being like an overlay system without actually overlaying.