The wiki shows a Block variant of the custom console. I’m at Year 38, I’ve done and unlocked just about everything; but this doesn’t show up as an option for me. Am I missing something?
Those custom consoles inages are very random.
You just need luck.
So if I keep reloading my save, is there a chance the options available to me will change?
No, I think You need create console to those images change.
I think you need to make 3 consoles before that one is there for you to make it, might be 2 
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eeeeyuppers. Resinex is correct. After releasing my second console, low and behold, there’s the block console!