These are a few of the reasons I've continued to use the "Open With" extension with mpv. ([right-click]->Open With->mpv) This provides full playback control, lets me toggle stay-on-top, etc. Firefox's PiP is a nice thought but just isn't right for me as currently implemented.
That's what I do as well, and it's fantastic. Bonus functionality: Get MPV to always open on the second screen fullscreen (if you have one) and have it be always-on-top, small and on the bottom right corner when non-fullscreen, so you can just press Esc on the full-screen mpv window and get a PiP-like window.
if you like vim like keybindings courtesy of tridactyl
bind V hint -W ! mpv to show a letter or letters adjacent to all links and open the one chosen in mpv. Normally most pages have few enough links visible that hints are either 1 or 2 characters. This means instead of picking up the mouse you can hit 3 keys.