you can cloak on the way through.
I have been going through in a blockade runner and a DST.
If the rats are on gate, MWD/Cloak with the DST is still a time to hold your breath because the frigates head toward you when you decloak from the gate cloak, but in a Blockade Runner it’s straight forward.
It seems so far the the invasions only last a day before they move. So if you can wait and do something else, then that works, however we don’t have much to go on yet in terms of how quickly they seem to move on to elsewhere.
The other thing would be to try luring them off gate with a scout. They will follow you so you can move their fleet to a different location it seems, but I haven’t tried that myself yet, so I might just be leading you to a loss with that advice. So far they don’t seem to jump gate with you. So you only need to worry about jumping into a system, not leaving it.