Plumbing a modified S/P Trap? With a Vent on the ‘P’?
As nobody else has come to the plate yet: reasons crown vents have been banned (for a long time) include (I'll community wiki, feel free to add, or write a whole new answer):

Easily plugged/blocked. You get a clog, you plunge it, the mass of hairy gook is sent directly from the trap into the vent line, the vent is now plugged. Your proposed setup is perfect for this problem.
High flow into the trap (draining a full sink, say) can cause the vent opening to be blocked by water, encouraging siphoning. With the vent further down the pipe, the water level in the pipe falls, leaving airspace at the top for the vent. Can also lead to gradual clogging if fats floating on the water congeal in the vent.
Several sources claim faster evaporation, but I don't know that I buy that argument.