I got stuck on a job in Dubai (Government client - they also had us work in trailers on-site - no remote access allowed) with a Remote Desktop jump host where the mouse didn't have any pass-through to my terminal session - which mean I had to work for 8 hours a day without any ability to select/copy/paste with a mouse. I had tmux-installed on the remote hosts and for the next three months, select/cut/copy/paste/resize panes/etc... were done without a mouse. Seven years later, I've never once used a mouse with tmux since then. https://github.com/schasse/tmux-jump is the equivalent plugin that lets you jump anywhere you want on the screen.
Yes - it's brilliant and I use it ~100 times/day when working with tmux.
https://github.com/schasse/tmux-jump
It's key concept is that you jump to the first letter/number of a "word" and then navigate from there, and, the keys in the label are on the home row. 95% of the time it's less than two characters - I've got the plugin mapped to Alt-u (no meta).
A very common keystroke pattern for me is Alt-u, couple characters (jumps to the exact spot on the screen I want to be), [space] (to start selecting) f (for the character I want to go to) and maybe a couple ; (jump to next instance of that letter) to get to where I want to go, [enter] to copy into the copy-buffer.
This also bothers me. As a keyboard guy it mostly bothered me that I could not jump to the thing that I wanted to copy. I found https://github.com/schasse/tmux-jump, which works really well with https://github.com/tmux-plugins/tmux-yank
I had the very same problem. Especially, I could not jump to the string I wanted to copy. I wrote a tmux plugin for it https://github.com/schasse/tmux-jump
Maybe it helps you too. Works great with https://github.com/tmux-plugins/tmux-yank
It's been one of my #1 terminal frustrations, too!!! But instead of relying on GUIs and the mouse, I started to use terminal tools and wrote a plugin for tmux that helped me. https://github.com/schasse/tmux-jump
Maybe it's useful for you.