I haven't really had issues with fzf in tmux. Personally I just write a couple of my own aliases on top of fzf and it works great. I have ^T bound to open fzf and then edit the file I pick in vim. For me I find that editing files and selecting files to add to my VCS are my two uses cases. The latter I solve with scm_breeze[0].

[0] https://github.com/ndbroadbent/scm_breeze