Are you controlling temperature? Cooler fermentation holds more CO2. When you dryhop, that CO2 comes out and will purge the headspace pretty quickly.
Commercially, we get the hops in as fast as we can and close up the very small port. If we don't, hilarity ensues!
https://www.youtube.com/watch?v=Zn2oQR5p_fcEven an 8" manway door is a relatively small opening compared to the total surface area. CO2 is heavier than air, so it doesn't come tumbling out when a port is opened at the top. If you can dryhop without taking off the whole lid, all the better.
For multiple dry hop schedules, you can take a CO2 hose and set it for a slow flow that you point into the headspace as you dryhop. That will keep a blanket on top of your beer. Obviously, you can add the hops very gently to avoid churning and splashing.