I was hoping a schooner owner would come in here, but as they haven't...
Running wing and wing: I got something similar with a ketch rig, the mizzen had to be sheeted in a bit, not let out square, to keep air flowing across it and keep the mainsail working. Schooner owners have been known to sheet their foresail hard amidships, as a roll and yaw damper, since its smaller size, is not so important to provide good drive downwind - the main does most of the work. With my ketch, it was the other way about: I reefed the mizzen to give the mainsail clear air.
Reefing when hard on the wind: I think that it's only rigs with heavy wooden battens that can get away without downhauls. Especially with wide sail panels. If this is the boat I think it is, I remember looking at photos and thinking that the masts looked woefully undersized, very spindly. They shouldn't bend appreciably, for use offshore; masts that whip about in a seaway are very unpleasant. I suggest that two spanned downhauls are fitted, one serving reefs 1 and 2, and one serving reefs 3 and 4, as a first step. There were experiments some years ago, doing away with them and relying on several LHPs to hold the sail to the mast. Is the whole sail blowing away from from the mast when not constrained by LHPs, or is it just that that the luffs of the lower panels are scalloped but the battens are held to the mast by batten parrels? The latter is not thought to be too harmful in flat sails, but would distort the shape of a cambered panel.