Wow you really went ham on this, thanks!

The table is not small small, more like narrow so there is just enough space for 4 players and their tablets and dice trays. We have erasable(?) grid map book in front of my side of the table (GM screen with laptop and dice tray behind, and that takes the whole width of the table).
We use miniatures (nothing fancy) to represent both PCs and NPCs but room boundaries are written on the grid with marker and that is about it, I do have some pane minis with stuff like rocks, pillars and trees but... reality is that my combats probably feel pretty barren when it comes to hiding/occlusion spots (now that I am thinking about this, I have probably not bothered because of this whole issue), I usually only sprinkle in stuff when it makes "logistical" sense to have it there.

Clipboard is actually really good idea for my setup, I can tuck it between the laptop and GM screen when not actively using and it is mostly out of the way for everything else.

I do like the init steps you take to resolve this, highest Perc DC vs lowest roll, if failed then note who sees who and go from there in the init order - to avoid longer pauses from me as GM.
I will probably return to your comment after we have to deal with stealth again lol.