The screenshot with tmux unsplit shows the cursor in the correct position, right?
On Secure Shell on my Linux workstation with the default font I'm able to get past 1k columns without cursor troubles, even in tmux with 4 vertical splits.
On a high-dpi display (Chromebook Pixel) I start to see cursor positioning issues early on, but only if I set the font size to nearly-unreadle. Are you on a high-dpi display, or just the builtin screen on the ARM Chromebook?
At this point my guess is that Proggy is missing the vertical bar character that tmux uses, and so the browser is finding it in a different font (with a different size).
Can you run alsamixer and see if it looks all screwey?
I've tried installing Proggy but I'm having trouble getting Chrome to see it. What's the font-face called? How'd you get it installed on your Chromebook, dev mode?
The reason this would trip up hterm but not gnome-terminal comes down to implementation. hterm has to trust the browser to render each character at the same size. The alternative is to render each character inside its own DOM node and explicitly set the size of that node. While that would provide a more robust display, the huge increase in DOM nodes would slow things down and blow up the memory requirements. Gnome-terminal is a native app and not subject to these constraints.
I'm not sure the best way to work around this. The quick answer is "don't use proggy", but I imagine you won't like that. This issue is likely to show up in other fonts too, so even if you're ok with this, it won't last.
From a quick read of the man page I don't see a tmux option to change the vertical bar character. We could potentially test for the missing graphic characters and translate them to ASCII graphics. It wouldn't be bulletproof, but would solve the main issue of "tmux screws up the cursor position" at least.
Rob.