How to handle stealth & detection without bogging it down?

Considering the last few posts are about stealth and detection I might as well kick this off:

I skip and short circuit stealth/detection as much as possible.

None of my players have built a stealth based characters - probably also because of the complexity with detection and the seemingly bad action econ when dealing with "actually getting Hidden".

I have two main problems with it:

• comparison explosion? Whenever you have to resolve who sees who (esp at init) you have to at worst compare a roll for each character on one side to all the perception DCs of the other side and this gets really slow for me [^1]
• tracking who currently sees who / at what detection levels they currently are to others

Any tips and tricks very much welcome:)

[^1]: Both me and PCs track chars digitally (pathbuilder) and it is definitely slow to gather this information quickly on a laptop. A sheet of paper with highlighted bonuses/DCs for both the party and NPCs would go a long way for this but our play table is rather small and already pretty packed :/