Amp has native clipboard integration, so content will carry between different instances. Configuring the register => clipboard was something I personally disliked when configuring Vim.

Amp also supports suspending (hit "z" in normal mode) as I use that workflow all the time. As for the small window issue, you can "zoom" a tmux panel with <leader>-z. I get that this is less than ideal if you're used to the suspend action collapsing all panes by default (and expanding them on resume). Workflows are tricky; to each their own, I guess! :)